Альфапедия

числение -calculus

редактировать

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    • 1.1 #1050;#1086;#1085;#1089;#1090;#1088;#1091;#1082;#1094;#1080;#1080; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072;
    • 1.2 #1053;#1077;#1073;#1086;#1083;#1100;#1096;#1086;#1081; #1087;#1088;#1080;#1084;#1077;#1088;
  • 2 #1060;#1086;#1088;#1084;#1072;#1083;#1100;#1085;#1086;#1077; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1077;#1085;#1080;#1077;
    • 2.1 #1057;#1080;#1085;#1090;#1072;#1082;#1089;#1080;#1089;
    • 2.2 #1057;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1085;#1086;#1077; #1089;#1086;#1086;#1090;#1074;#1077;#1090;#1089;#1090;#1074;#1080;#1077;
    • 2.3 #1057;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1072; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;
    • 2.4 #1055;#1086;#1074;#1090;#1086;#1088;#1085;#1099;#1081; #1087;#1088;#1080;#1084;#1077;#1088;
    • 2.5 #1055;#1086;#1084;#1077;#1095;#1077;#1085;#1085;#1072;#1103; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1072;
  • 3 #1056;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1103; #1080; #1074;#1072;#1088;#1080;#1072;#1085;#1090;#1099;
  • 4 #1089;#1074;#1086;#1081;#1089;#1090;#1074;#1072;
    • 4.1 #1055;#1086;#1083;#1085;#1086;#1090;#1072; #1087;#1086; #1058;#1100;#1102;#1088;#1080;#1085;#1075;#1091;
  • 5 #1041;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1080; #1074; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1080;
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    • 5.2 #1054;#1090;#1082;#1088;#1099;#1090;#1086;#1077; #1076;#1074;#1086;#1081;#1085;#1086;#1077; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086;
      • 5.2.1 #1056;#1072;#1085;#1085;#1077;#1077;, #1087;#1086;#1079;#1076;#1085;#1077;#1077; #1080; #1086;#1090;#1082;#1088;#1099;#1090;#1086;#1077; #1076;#1074;#1086;#1081;#1085;#1086;#1077; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086; #1088;#1072;#1079;#1083;#1080;#1095;#1072;#1102;#1090;#1089;#1103;.
    • 5.3 #1050;#1086;#1083;#1102;#1095;#1072;#1103; #1101;#1082;#1074;#1080;#1074;#1072;#1083;#1077;#1085;#1090;#1085;#1086;#1089;#1090;#1100;
  • 6 #1087;#1088;#1080;#1083;#1086;#1078;#1077;#1085;#1080;#1081;
  • 7 #1048;#1089;#1090;#1086;#1088;#1080;#1103;
  • 8 #1056;#1077;#1072;#1083;#1080;#1079;#1072;#1094;#1080;#1080;
  • 9 #1055;#1088;#1080;#1084;#1077;#1095;#1072;#1085;#1080;#1103;
  • 10 #1057;#1089;#1099;#1083;#1082;#1080;
  • 11 #1042;#1085;#1077;#1096;#1085;#1080;#1077; #1089;#1089;#1099;#1083;#1082;#1080;
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  • #1086;#1073;#1097;#1077;#1085;#1080;#1077;, #1075;#1076;#1077;
    • #1087;#1088;#1077;#1092;#1080;#1082;#1089; #1074;#1074;#1086;#1076;#1072; - #1101;#1090;#1086; #1087;#1088;#1086;#1094;#1077;#1089;#1089;, #1086;#1078;#1080;#1076;#1072;#1102;#1097;#1080;#1081; #1089;#1086;#1086;#1073;#1097;#1077;#1085;#1080;#1103;, #1082;#1086;#1090;#1086;#1088;#1086;#1077; #1073;#1099;#1083;#1086; #1086;#1090;#1087;#1088;#1072;#1074;#1083;#1077;#1085;#1086; #1087;#1086; #1082;#1072;#1085;#1072;#1083;#1091; #1089;#1074;#1103;#1079;#1080; #1089; #1080;#1084;#1077;#1085;#1077;#1084;, #1087;#1088;#1077;#1078;#1076;#1077; #1095;#1077;#1084; #1087;#1088;#1086;#1076;#1086;#1083;#1078;#1080;#1090;#1100; #1082;#1072;#1082;, #1089;#1074;#1103;#1079;#1099;#1074;#1072;#1103; #1087;#1086;#1083;#1091;#1095;#1077;#1085;#1085;#1086;#1077; #1080;#1084;#1103; #1089; #1080;#1084;#1077;#1085;#1077;#1084; x. #1054;#1073;#1099;#1095;#1085;#1086; #1101;#1090;#1086; #1084;#1086;#1076;#1077;#1083;#1080;#1088;#1091;#1077;#1090; #1083;#1080;#1073;#1086; #1087;#1088;#1086;#1094;#1077;#1089;#1089;, #1086;#1078;#1080;#1076;#1072;#1102;#1097;#1080;#1081; #1089;#1074;#1103;#1079;#1080; #1086;#1090; #1089;#1077;#1090;#1080;, #1083;#1080;#1073;#1086; #1084;#1077;#1090;#1082;#1091;, #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1091;#1077;#1084;#1091;#1102; #1086;#1087;#1077;#1088;#1072;#1094;#1080;#1077;#1081; #1090;#1086;#1083;#1100;#1082;#1086; #1086;#1076;#1080;#1085; #1088;#1072;#1079;. c ( #1048;#1082;#1089; ) . #1087; {\ Displaystyle #1089; \ #1074;#1083;#1077;#1074;#1086; (#1093; \ #1074;#1087;#1088;#1072;#1074;#1086;).P} c {\ displaystyle c} #1087; {\ displaystyle P}cgoto c
    • #1087;#1088;#1077;#1092;#1080;#1082;#1089; output #1086;#1087;#1080;#1089;#1099;#1074;#1072;#1077;#1090;, #1095;#1090;#1086; #1080;#1084;#1103; #1087;#1077;#1088;#1077;#1076;#1072;#1077;#1090;#1089;#1103; #1087;#1086; #1082;#1072;#1085;#1072;#1083;#1091; #1087;#1077;#1088;#1077;#1076; #1087;#1088;#1086;#1076;#1086;#1083;#1078;#1077;#1085;#1080;#1077;#1084; #1082;#1072;#1082;. #1050;#1072;#1082; #1087;#1088;#1072;#1074;#1080;#1083;#1086;, #1101;#1090;#1086; #1084;#1086;#1076;#1077;#1083;#1080; #1086;#1090;#1087;#1088;#1072;#1074;#1082;#1080; #1089;#1086;#1086;#1073;#1097;#1077;#1085;#1080;#1103; #1087;#1086; #1089;#1077;#1090;#1080; #1080;#1083;#1080; #1086;#1087;#1077;#1088;#1072;#1094;#1080;#1080;. c macr; #10216; #1091; #10217; . #1087; {\ displaystyle {\ overline {c}} \ langle y \ rangle.P} #1091; {\ displaystyle y} c {\ displaystyle c} #1087; {\ displaystyle P}goto c
  • #1088;#1077;#1087;#1083;#1080;#1082;#1072;#1094;#1080;#1103;, #1079;#1072;#1087;#1080;#1089;#1072;#1085;#1085;#1072;#1103;, #1082;#1086;#1090;#1086;#1088;#1091;#1102; #1084;#1086;#1078;#1085;#1086; #1088;#1072;#1089;#1089;#1084;#1072;#1090;#1088;#1080;#1074;#1072;#1090;#1100; #1082;#1072;#1082; #1087;#1088;#1086;#1094;#1077;#1089;#1089;, #1082;#1086;#1090;#1086;#1088;#1099;#1081; #1074;#1089;#1077;#1075;#1076;#1072; #1084;#1086;#1078;#1077;#1090; #1089;#1086;#1079;#1076;#1072;#1090;#1100; #1085;#1086;#1074;#1091;#1102; #1082;#1086;#1087;#1080;#1102;. #1050;#1072;#1082; #1087;#1088;#1072;#1074;#1080;#1083;#1086;, #1101;#1090;#1086; #1084;#1086;#1076;#1077;#1083;#1080;#1088;#1091;#1077;#1090; #1083;#1080;#1073;#1086; #1089;#1077;#1090;#1077;#1074;#1086;#1081; #1089;#1077;#1088;#1074;#1080;#1089;, #1083;#1080;#1073;#1086; #1084;#1077;#1090;#1082;#1091;, #1086;#1078;#1080;#1076;#1072;#1102;#1097;#1091;#1102; #1083;#1102;#1073;#1086;#1075;#1086; #1082;#1086;#1083;#1080;#1095;#1077;#1089;#1090;#1074;#1072; #1086;#1087;#1077;#1088;#1072;#1094;#1080;#1081;. ! #1087; {\ Displaystyle! \, P} #1087; {\ displaystyle P}cgoto c
  • #1089;#1086;#1079;#1076;#1072;#1085;#1080;#1077; #1085;#1086;#1074;#1086;#1075;#1086; #1079;#1072;#1087;#1080;#1089;#1072;#1085;#1085;#1086;#1075;#1086; #1080;#1084;#1077;#1085;#1080;, #1082;#1086;#1090;#1086;#1088;#1086;#1077; #1084;#1086;#1078;#1085;#1086; #1088;#1072;#1089;#1089;#1084;#1072;#1090;#1088;#1080;#1074;#1072;#1090;#1100; #1082;#1072;#1082; #1087;#1088;#1086;#1094;#1077;#1089;#1089;, #1074;#1099;#1076;#1077;#1083;#1103;#1102;#1097;#1080;#1081; #1074;#1085;#1091;#1090;#1088;#1080; #1085;#1086;#1074;#1091;#1102; #1082;#1086;#1085;#1089;#1090;#1072;#1085;#1090;#1091; x. #1050;#1086;#1085;#1089;#1090;#1072;#1085;#1090;#1099; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1103;#1102;#1090;#1089;#1103; #1090;#1086;#1083;#1100;#1082;#1086; #1089;#1074;#1086;#1080;#1084;#1080; #1080;#1084;#1077;#1085;#1072;#1084;#1080; #1080; #1074;#1089;#1077;#1075;#1076;#1072; #1103;#1074;#1083;#1103;#1102;#1090;#1089;#1103; #1082;#1072;#1085;#1072;#1083;#1072;#1084;#1080; #1089;#1074;#1103;#1079;#1080;. #1057;#1086;#1079;#1076;#1072;#1085;#1080;#1077; #1085;#1086;#1074;#1086;#1075;#1086; #1080;#1084;#1077;#1085;#1080; #1074; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1077; #1090;#1072;#1082;#1078;#1077; #1085;#1072;#1079;#1099;#1074;#1072;#1077;#1090;#1089;#1103; #1086;#1075;#1088;#1072;#1085;#1080;#1095;#1077;#1085;#1080;#1077;#1084;. ( nu; #1048;#1082;#1089; ) #1087; {\ Displaystyle \ #1074;#1083;#1077;#1074;#1086; (\ #1085;#1102; #1093; \ #1074;#1087;#1088;#1072;#1074;#1086;) P} #1087; {\ displaystyle P}
  • #1079;#1072;#1087;#1080;#1089;#1072;#1085;#1085;#1099;#1081; #1087;#1088;#1086;#1094;#1077;#1089;#1089; nil - #1101;#1090;#1086; #1087;#1088;#1086;#1094;#1077;#1089;#1089;, #1074;#1099;#1087;#1086;#1083;#1085;#1077;#1085;#1080;#1077; #1082;#1086;#1090;#1086;#1088;#1086;#1075;#1086; #1079;#1072;#1074;#1077;#1088;#1096;#1077;#1085;#1086; #1080; #1086;#1089;#1090;#1072;#1085;#1086;#1074;#1083;#1077;#1085;#1086;. 0 {\ displaystyle 0}

#1061;#1086;#1090;#1103; #1084;#1080;#1085;#1080;#1084;#1072;#1083;#1080;#1079;#1084; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103; #1085;#1077; #1087;#1086;#1079;#1074;#1086;#1083;#1103;#1077;#1090; #1085;#1072;#1084; #1087;#1080;#1089;#1072;#1090;#1100; #1087;#1088;#1086;#1075;#1088;#1072;#1084;#1084;#1099; #1074; #1086;#1073;#1099;#1095;#1085;#1086;#1084; #1089;#1084;#1099;#1089;#1083;#1077;, #1077;#1075;#1086; #1083;#1077;#1075;#1082;#1086; #1088;#1072;#1089;#1096;#1080;#1088;#1080;#1090;#1100;. #1042; #1095;#1072;#1089;#1090;#1085;#1086;#1089;#1090;#1080;, #1083;#1077;#1075;#1082;#1086; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1080;#1090;#1100; #1082;#1072;#1082; #1091;#1087;#1088;#1072;#1074;#1083;#1103;#1102;#1097;#1080;#1077; #1089;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1099;, #1090;#1072;#1082;#1080;#1077; #1082;#1072;#1082; #1088;#1077;#1082;#1091;#1088;#1089;#1080;#1103;, #1094;#1080;#1082;#1083;#1099; #1080; #1087;#1086;#1089;#1083;#1077;#1076;#1086;#1074;#1072;#1090;#1077;#1083;#1100;#1085;#1072;#1103; #1082;#1086;#1084;#1087;#1086;#1079;#1080;#1094;#1080;#1103;, #1090;#1072;#1082; #1080; #1090;#1080;#1087;#1099; #1076;#1072;#1085;#1085;#1099;#1093;, #1090;#1072;#1082;#1080;#1077; #1082;#1072;#1082; #1092;#1091;#1085;#1082;#1094;#1080;#1080; #1087;#1077;#1088;#1074;#1086;#1075;#1086; #1087;#1086;#1088;#1103;#1076;#1082;#1072;, #1079;#1085;#1072;#1095;#1077;#1085;#1080;#1103; #1080;#1089;#1090;#1080;#1085;#1085;#1086;#1089;#1090;#1080;, #1089;#1087;#1080;#1089;#1082;#1080; #1080; #1094;#1077;#1083;#1099;#1077; #1095;#1080;#1089;#1083;#1072;. #1041;#1086;#1083;#1077;#1077; #1090;#1086;#1075;#1086;, #1073;#1099;#1083;#1080; #1087;#1088;#1077;#1076;#1083;#1086;#1078;#1077;#1085;#1099; #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1103; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103;, #1082;#1086;#1090;#1086;#1088;#1099;#1077; #1091;#1095;#1080;#1090;#1099;#1074;#1072;#1102;#1090; #1088;#1072;#1089;#1087;#1088;#1077;#1076;#1077;#1083;#1077;#1085;#1080;#1077; #1080;#1083;#1080; #1082;#1088;#1080;#1087;#1090;#1086;#1075;#1088;#1072;#1092;#1080;#1102; #1089; #1086;#1090;#1082;#1088;#1099;#1090;#1099;#1084; #1082;#1083;#1102;#1095;#1086;#1084;. #1055;#1088;#1080;#1083;#1086;#1078;#1077;#1085;#1085;#1086;#1077; pi; -#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103; #1080;#1079; - #1040;#1073;#1072;#1076;#1080; #1080; #1046;.#1060;#1091;#1088;#1085;#1100;#1077; [1] #1087;#1086;#1084;#1077;#1089;#1090;#1080;#1090;#1100; #1101;#1090;#1080; #1088;#1072;#1079;#1083;#1080;#1095;#1085;#1099;#1077; #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1103; #1085;#1072; #1092;#1086;#1088;#1084;#1072;#1083;#1100;#1085;#1086;#1081; #1086;#1089;#1085;#1086;#1074;#1077; #1087;#1086;#1089;#1088;#1077;#1076;#1089;#1090;#1074;#1086;#1084; #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1103; pi; -#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103; #1089; #1087;#1088;#1086;#1080;#1079;#1074;#1086;#1083;#1100;#1085;#1099;#1084;#1080; #1090;#1080;#1087;#1072;#1084;#1080; #1076;#1072;#1085;#1085;#1099;#1093;.

#1053;#1077;#1073;#1086;#1083;#1100;#1096;#1086;#1081; #1087;#1088;#1080;#1084;#1077;#1088;

#1053;#1080;#1078;#1077; #1087;#1088;#1080;#1074;#1077;#1076;#1077;#1085; #1082;#1088;#1086;#1096;#1077;#1095;#1085;#1099;#1081; #1087;#1088;#1080;#1084;#1077;#1088; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072;, #1082;#1086;#1090;#1086;#1088;#1099;#1081; #1089;#1086;#1089;#1090;#1086;#1080;#1090; #1080;#1079; #1090;#1088;#1077;#1093; #1087;#1072;#1088;#1072;#1083;#1083;#1077;#1083;#1100;#1085;#1099;#1093; #1082;#1086;#1084;#1087;#1086;#1085;#1077;#1085;#1090;#1086;#1074;. #1048;#1084;#1103; #1082;#1072;#1085;#1072;#1083;#1072; x #1080;#1079;#1074;#1077;#1089;#1090;#1085;#1086; #1090;#1086;#1083;#1100;#1082;#1086; #1087;#1077;#1088;#1074;#1099;#1084; #1076;#1074;#1091;#1084; #1082;#1086;#1084;#1087;#1086;#1085;#1077;#1085;#1090;#1072;#1084;.

( nu; #1048;#1082;#1089; ) ( #1048;#1082;#1089; macr; #10216; z #10217; . 0 | #1048;#1082;#1089; ( #1091; ) . #1091; macr; #10216; #1048;#1082;#1089; #10217; . #1048;#1082;#1089; ( #1091; ) . 0 ) | z ( v ) . v macr; #10216; v #10217; .0 {\ Displaystyle {\ begin {align} (\ nu x) amp; \; (\; {\ overline {x}} \ langle z \ rangle. \; 0 \\ amp; \; | \; x (y). \ ; {\ overline {y}} \ langle x \ rangle. \; x (y). \; 0 \;) \\ amp; \; | \; z (v). \; {\ overline {v}} \ langle v \ rangle.0 \ end {align}}}

#1055;#1077;#1088;#1074;#1099;#1077; #1076;#1074;#1072; #1082;#1086;#1084;#1087;#1086;#1085;#1077;#1085;#1090;#1072; #1084;#1086;#1075;#1091;#1090; #1086;#1073;#1084;#1077;#1085;#1080;#1074;#1072;#1090;#1100;#1089;#1103; #1076;#1072;#1085;#1085;#1099;#1084;#1080; #1087;#1086; #1082;#1072;#1085;#1072;#1083;#1091; x, #1080; #1080;#1084;#1103; y #1089;#1090;#1072;#1085;#1086;#1074;#1080;#1090;#1089;#1103; #1087;#1088;#1080;#1074;#1103;#1079;#1072;#1085;#1085;#1099;#1084; #1082; z. #1055;#1086;#1101;#1090;#1086;#1084;#1091; #1089;#1083;#1077;#1076;#1091;#1102;#1097;#1080;#1084; #1096;#1072;#1075;#1086;#1084; #1074; #1101;#1090;#1086;#1084; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1077; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103;

( nu; #1048;#1082;#1089; ) ( 0 | z macr; #10216; #1048;#1082;#1089; #10217; . #1048;#1082;#1089; ( #1091; ) . 0 ) | z ( v ) . v macr; #10216; v #10217; . 0 {\ Displaystyle {\ begin {align} (\ nu x) amp; \; (\; 0 \\ amp; \; | \; {\ overline {z}} \ langle x \ rangle. \; x (y). \ ; 0 \;) \\ amp; \; | \; z (v). \; {\ Overline {v}} \ langle v \ rangle. \; 0 \ end {align}}}

#1054;#1073;#1088;#1072;#1090;#1080;#1090;#1077; #1074;#1085;#1080;#1084;#1072;#1085;#1080;#1077;, #1095;#1090;#1086; #1086;#1089;#1090;#1072;#1074;#1096;#1080;#1081;#1089;#1103; y #1085;#1077; #1080;#1079;#1084;#1077;#1085;#1103;#1077;#1090;#1089;#1103;, #1087;#1086;#1090;#1086;#1084;#1091; #1095;#1090;#1086; #1086;#1085; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1077;#1085; #1074;#1086; #1074;#1085;#1091;#1090;#1088;#1077;#1085;#1085;#1077;#1081; #1086;#1073;#1083;#1072;#1089;#1090;#1080;. #1042;#1090;#1086;#1088;#1086;#1081; #1080; #1090;#1088;#1077;#1090;#1080;#1081; #1087;#1072;#1088;#1072;#1083;#1083;#1077;#1083;#1100;#1085;#1099;#1077; #1082;#1086;#1084;#1087;#1086;#1085;#1077;#1085;#1090;#1099; #1090;#1077;#1087;#1077;#1088;#1100; #1084;#1086;#1075;#1091;#1090; #1086;#1073;#1084;#1077;#1085;#1080;#1074;#1072;#1090;#1100;#1089;#1103; #1076;#1072;#1085;#1085;#1099;#1084;#1080; #1087;#1086; #1080;#1084;#1077;#1085;#1080; #1082;#1072;#1085;#1072;#1083;#1072; z, #1072; #1080;#1084;#1103; v #1089;#1090;#1072;#1085;#1086;#1074;#1080;#1090;#1089;#1103; #1087;#1088;#1080;#1074;#1103;#1079;#1072;#1085;#1085;#1099;#1084; #1082; x. #1057;#1083;#1077;#1076;#1091;#1102;#1097;#1080;#1081; #1096;#1072;#1075; #1074; #1101;#1090;#1086;#1084; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1077; #1089;#1077;#1081;#1095;#1072;#1089;

( nu; #1048;#1082;#1089; ) ( 0 | #1048;#1082;#1089; ( #1091; ) . 0 | #1048;#1082;#1089; macr; #10216; #1048;#1082;#1089; #10217; . 0 ) {\ Displaystyle {\ begin {align} (\ nu x) amp; \; (\; 0 \\ amp; \; | \; x (y). \; 0 \\ amp; \; | \; {\ overline {x }} \ langle x \ rangle. \; 0 \;) \ end {#1074;#1099;#1088;#1072;#1074;#1085;#1080;#1074;#1072;#1077;#1090;#1089;#1103;}}}

#1054;#1073;#1088;#1072;#1090;#1080;#1090;#1077; #1074;#1085;#1080;#1084;#1072;#1085;#1080;#1077;, #1095;#1090;#1086;, #1087;#1086;#1089;#1082;#1086;#1083;#1100;#1082;#1091; #1083;#1086;#1082;#1072;#1083;#1100;#1085;#1086;#1077; #1080;#1084;#1103; x #1073;#1099;#1083;#1086; #1074;#1099;#1074;#1077;#1076;#1077;#1085;#1086;, #1086;#1073;#1083;#1072;#1089;#1090;#1100; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1103; x #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1072;, #1095;#1090;#1086;#1073;#1099; #1086;#1093;#1074;#1072;#1090;#1080;#1090;#1100; #1090;#1072;#1082;#1078;#1077; #1090;#1088;#1077;#1090;#1080;#1081; #1082;#1086;#1084;#1087;#1086;#1085;#1077;#1085;#1090;. #1053;#1072;#1082;#1086;#1085;#1077;#1094;, #1082;#1072;#1085;#1072;#1083; x #1084;#1086;#1078;#1085;#1086; #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1086;#1074;#1072;#1090;#1100; #1076;#1083;#1103; #1086;#1090;#1087;#1088;#1072;#1074;#1082;#1080; #1080;#1084;#1077;#1085;#1080; x. #1055;#1086;#1089;#1083;#1077; #1101;#1090;#1086;#1075;#1086; #1074;#1089;#1077; #1086;#1076;#1085;#1086;#1074;#1088;#1077;#1084;#1077;#1085;#1085;#1086; #1074;#1099;#1087;#1086;#1083;#1085;#1103;#1102;#1097;#1080;#1077;#1089;#1103; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1099; #1086;#1089;#1090;#1072;#1085;#1086;#1074;#1080;#1083;#1080;#1089;#1100;.

( nu; #1048;#1082;#1089; ) ( 0 | 0 | 0 ) {\ Displaystyle {\ begin {#1074;#1099;#1088;#1086;#1074;#1085;#1077;#1085;#1086;} (\ #1085;#1102; #1093;) amp; \; (\; 0 \\ amp; \; | \; 0 \\ amp; \; | \; 0 \;) \ #1082;#1086;#1085;#1077;#1094; {#1074;#1099;#1088;#1086;#1074;#1085;#1077;#1085;#1086;}}}
#1060;#1086;#1088;#1084;#1072;#1083;#1100;#1085;#1086;#1077; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1077;#1085;#1080;#1077;

#1057;#1080;#1085;#1090;#1072;#1082;#1089;#1080;#1089;

#1055;#1091;#1089;#1090;#1100; Chi; #1073;#1091;#1076;#1077;#1090; #1085;#1072;#1073;#1086;#1088;#1086;#1084; #1086;#1073;#1098;#1077;#1082;#1090;#1086;#1074;, #1085;#1072;#1079;#1099;#1074;#1072;#1077;#1084;#1099;#1093; #1080;#1084;#1077;#1085;#1072;#1084;#1080;. #1040;#1073;#1089;#1090;#1088;#1072;#1082;#1090;#1085;#1099;#1081; #1089;#1080;#1085;#1090;#1072;#1082;#1089;#1080;#1089; #1076;#1083;#1103; pi; -#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103; #1087;#1086;#1089;#1090;#1088;#1086;#1077;#1085; #1080;#1079; #1089;#1083;#1077;#1076;#1091;#1102;#1097;#1077;#1081; #1075;#1088;#1072;#1084;#1084;#1072;#1090;#1080;#1082;#1080; BNF (#1075;#1076;#1077; #1093; #1080; #1091; #1103;#1074;#1083;#1103;#1102;#1090;#1089;#1103; #1083;#1102;#1073;#1099;#1084;#1080; #1080;#1084;#1077;#1085;#1072;#1084;#1080; #1080;#1079; #1049;):

#1087; , Q #1079;#1085;#1072;#1082; #1088;#1072;#1074;#1085;#1086; #1048;#1082;#1089; ( #1091; ) . #1087; #1055;#1086;#1083;#1091;#1095;#1072;#1090;#1100; #1085;#1072; #1082;#1072;#1085;#1072;#1083;#1077; #1048;#1082;#1089; , #1087;#1088;#1080;#1074;#1103;#1078;#1080;#1090;#1077; #1088;#1077;#1079;#1091;#1083;#1100;#1090;#1072;#1090; #1082; #1091; , #1079;#1072;#1090;#1077;#1084; #1079;#1072;#1087;#1091;#1089;#1090;#1080;#1090;#1077; #1087; | #1048;#1082;#1089; macr; #10216; #1091; #10217; . #1087; #1054;#1090;#1087;#1088;#1072;#1074;#1080;#1090;#1100; #1079;#1085;#1072;#1095;#1077;#1085;#1080;#1077; #1091; #1087;#1086; #1082;#1072;#1085;#1072;#1083;#1091; #1048;#1082;#1089; , #1079;#1072;#1090;#1077;#1084; #1079;#1072;#1087;#1091;#1089;#1090;#1080;#1090;#1077; #1087; | #1087; | Q #1047;#1072;#1087;#1091;#1089;#1090;#1080;#1090;#1100; #1087; #1072; #1090;#1072;#1082;#1078;#1077; Q #1086;#1076;#1085;#1086;#1074;#1088;#1077;#1084;#1077;#1085;#1085;#1086; | ( nu; #1048;#1082;#1089; ) #1087; #1057;#1086;#1079;#1076;#1072;#1090;#1100; #1085;#1086;#1074;#1099;#1081; #1082;#1072;#1085;#1072;#1083; #1048;#1082;#1089; #1080; #1073;#1077;#1075;#1080; #1087; | ! #1087; #1053;#1077;#1086;#1076;#1085;#1086;#1082;#1088;#1072;#1090;#1085;#1086; #1087;#1086;#1088;#1086;#1078;#1076;#1072;#1102;#1090;#1089;#1103; #1082;#1086;#1087;#1080;#1080; #1087; | 0 #1047;#1072;#1074;#1077;#1088;#1096;#1080;#1090;#1100; #1087;#1088;#1086;#1094;#1077;#1089;#1089; {\ displaystyle {\ begin {align} P, Q:: = amp; \; x (y).P \, \, \, \, \, amp; {\ text {#1055;#1086;#1083;#1091;#1095;#1077;#1085;#1080;#1077; #1087;#1086; #1082;#1072;#1085;#1072;#1083;#1091;}} x {\ text {, #1087;#1088;#1080;#1074;#1103;#1078;#1080;#1090;#1077; #1088;#1077;#1079;#1091;#1083;#1100;#1090;#1072;#1090; #1082;}} y {\ text {, #1079;#1072;#1090;#1077;#1084; #1079;#1072;#1087;#1091;#1089;#1090;#1080;#1090;#1077;}} P \\ amp; \; | \; {\ overline {x}} \ langle y \ rangle.P \, \, \, \, \, amp; {\ text {#1054;#1090;#1087;#1088;#1072;#1074;#1080;#1090;#1100; #1079;#1085;#1072;#1095;#1077;#1085;#1080;#1077;}} y {\ text {over channel}} x {\ text {, #1079;#1072;#1090;#1077;#1084; #1079;#1072;#1087;#1091;#1089;#1090;#1080;#1090;#1100;}} P \\ amp; \; | \; P | Q \, \, \, \, \, \, \, \, \, amp; {\ text {#1042;#1099;#1087;#1086;#1083;#1085;#1080;#1090;#1100;}} P {\ text {and}} Q {\ text {#1086;#1076;#1085;#1086;#1074;#1088;#1077;#1084;#1077;#1085;#1085;#1086;}} \\ amp; \; | \; (\ nu x) P \, \, \, amp; {\ text {#1057;#1086;#1079;#1076;#1072;#1090;#1100; #1085;#1086;#1074;#1099;#1081; #1082;#1072;#1085;#1072;#1083;}} x {\ text {#1080; #1079;#1072;#1087;#1091;#1089;#1090;#1080;#1090;#1100;}} P \\ amp; \; | \ ;! P \, \, \, amp; {\ text {#1053;#1077;#1086;#1076;#1085;#1086;#1082;#1088;#1072;#1090;#1085;#1086; #1089;#1086;#1079;#1076;#1072;#1074;#1072;#1090;#1100; #1082;#1086;#1087;#1080;#1080;}} P \\ amp; \; | \; 0 amp; {\ text {#1047;#1072;#1074;#1077;#1088;#1096;#1080;#1090;#1100; #1087;#1088;#1086;#1094;#1077;#1089;#1089;}} \ end {align}}}

#1042; #1082;#1086;#1085;#1082;#1088;#1077;#1090;#1085;#1086;#1084; #1089;#1080;#1085;#1090;#1072;#1082;#1089;#1080;#1089;#1077; #1085;#1080;#1078;#1077; #1087;#1088;#1077;#1092;#1080;#1082;#1089;#1099; #1089;#1074;#1103;#1079;#1099;#1074;#1072;#1102;#1090;#1089;#1103; #1073;#1086;#1083;#1077;#1077; #1087;#1083;#1086;#1090;#1085;#1086;, #1095;#1077;#1084; #1087;#1072;#1088;#1072;#1083;#1083;#1077;#1083;#1100;#1085;#1072;#1103; #1082;#1086;#1084;#1087;#1086;#1079;#1080;#1094;#1080;#1103; (|), #1072; #1089;#1082;#1086;#1073;#1082;#1080; #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1091;#1102;#1090;#1089;#1103; #1076;#1083;#1103; #1091;#1089;#1090;#1088;#1072;#1085;#1077;#1085;#1080;#1103; #1085;#1077;#1086;#1076;#1085;#1086;#1079;#1085;#1072;#1095;#1085;#1086;#1089;#1090;#1080;.

#1048;#1084;#1077;#1085;#1072; #1089;#1074;#1103;#1079;#1072;#1085;#1099; #1082;#1086;#1085;#1089;#1090;#1088;#1091;#1082;#1094;#1080;#1103;#1084;#1080; #1086;#1075;#1088;#1072;#1085;#1080;#1095;#1077;#1085;#1080;#1103; #1080; #1074;#1093;#1086;#1076;#1085;#1086;#1075;#1086; #1087;#1088;#1077;#1092;#1080;#1082;#1089;#1072;. #1060;#1086;#1088;#1084;#1072;#1083;#1100;#1085;#1086;, #1084;#1085;#1086;#1078;#1077;#1089;#1090;#1074;#1086; #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1099;#1093; #1080;#1084;#1077;#1085; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072; #1074; pi; ndash; #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1080; #1080;#1085;#1076;#1091;#1082;#1090;#1080;#1074;#1085;#1086; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1103;#1077;#1090;#1089;#1103; #1090;#1072;#1073;#1083;#1080;#1094;#1077;#1081; #1085;#1080;#1078;#1077;. #1053;#1072;#1073;#1086;#1088; #1089;#1074;#1103;#1079;#1072;#1085;#1085;#1099;#1093; #1080;#1084;#1077;#1085; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1103;#1077;#1090;#1089;#1103; #1082;#1072;#1082; #1080;#1084;#1077;#1085;#1072; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072;, #1085;#1077; #1074;#1093;#1086;#1076;#1103;#1097;#1080;#1077; #1074; #1085;#1072;#1073;#1086;#1088; #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1099;#1093; #1080;#1084;#1077;#1085;.

#1055;#1086;#1089;#1090;#1088;#1086;#1080;#1090;#1100; #1041;#1077;#1089;#1087;#1083;#1072;#1090;#1085;#1099;#1077; #1080;#1084;#1077;#1085;#1072;
0 {\ displaystyle 0} #1053;#1080;#1082;#1090;#1086;
#1072; macr; #10216; #1048;#1082;#1089; #10217; . #1087; {\ displaystyle {\ overline {a}} \ langle x \ rangle.P} #1072; ; #1093; ; #1074;#1089;#1077; #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1099;#1077; #1080;#1084;#1077;#1085;#1072; P
#1072; ( #1048;#1082;#1089; ) . #1087; {\ Displaystyle #1072; (#1093;).P} #1072; ; #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1099;#1077; #1080;#1084;#1077;#1085;#1072; P #1079;#1072; #1080;#1089;#1082;#1083;#1102;#1095;#1077;#1085;#1080;#1077;#1084; x
#1087; | Q {\ displaystyle P | Q} #1042;#1089;#1077; #1073;#1077;#1089;#1087;#1083;#1072;#1090;#1085;#1099;#1077; #1080;#1084;#1077;#1085;#1072; P #1080; Q
( nu; #1048;#1082;#1089; ) . #1087; {\ Displaystyle (\ #1085;#1102; #1093;).P} #1057;#1074;#1086;#1073;#1086;#1076;#1085;#1099;#1077; #1080;#1084;#1077;#1085;#1072; P, #1082;#1088;#1086;#1084;#1077; x
! #1087; {\ displaystyle! P} #1042;#1089;#1077; #1073;#1077;#1089;#1087;#1083;#1072;#1090;#1085;#1099;#1077; #1080;#1084;#1077;#1085;#1072; P

#1057;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1085;#1086;#1077; #1089;#1086;#1086;#1090;#1074;#1077;#1090;#1089;#1090;#1074;#1080;#1077;

#1062;#1077;#1085;#1090;#1088;#1072;#1083;#1100;#1085;#1099;#1084; #1082;#1072;#1082; #1076;#1083;#1103; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1080; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;, #1090;#1072;#1082; #1080; #1076;#1083;#1103; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1080; #1087;#1086;#1084;#1077;#1095;#1077;#1085;#1085;#1099;#1093; #1087;#1077;#1088;#1077;#1093;#1086;#1076;#1086;#1074; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1087;#1086;#1085;#1103;#1090;#1080;#1077; #1089;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1085;#1086;#1081; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1086;#1089;#1090;#1080;. #1044;#1074;#1072; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072; #1089;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1085;#1086; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1099;, #1077;#1089;#1083;#1080; #1086;#1085;#1080; #1080;#1076;#1077;#1085;#1090;#1080;#1095;#1085;#1099; #1087;#1086; #1089;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1077;. #1042; #1095;#1072;#1089;#1090;#1085;#1086;#1089;#1090;#1080;, #1087;#1072;#1088;#1072;#1083;#1083;#1077;#1083;#1100;#1085;#1072;#1103; #1082;#1086;#1084;#1087;#1086;#1079;#1080;#1094;#1080;#1103; #1082;#1086;#1084;#1084;#1091;#1090;#1072;#1090;#1080;#1074;#1085;#1072; #1080; #1072;#1089;#1089;#1086;#1094;#1080;#1072;#1090;#1080;#1074;#1085;#1072;.

#1058;#1086;#1095;#1085;#1077;#1077;, #1089;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1085;#1072;#1103; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1086;#1089;#1090;#1100; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1103;#1077;#1090;#1089;#1103; #1082;#1072;#1082; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1077; #1085;#1072;#1080;#1084;#1077;#1085;#1100;#1096;#1077;#1081; #1101;#1082;#1074;#1080;#1074;#1072;#1083;#1077;#1085;#1090;#1085;#1086;#1089;#1090;#1080;, #1089;#1086;#1093;#1088;#1072;#1085;#1103;#1077;#1084;#1086;#1077; #1082;#1086;#1085;#1089;#1090;#1088;#1091;#1082;#1094;#1080;#1103;#1084;#1080; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072; #1080; #1091;#1076;#1086;#1074;#1083;#1077;#1090;#1074;#1086;#1088;#1103;#1102;#1097;#1077;#1077;:

#1040;#1083;#1100;#1092;#1072;-#1087;#1088;#1077;#1086;#1073;#1088;#1072;#1079;#1086;#1074;#1072;#1085;#1080;#1077;:

  • #1087; equiv; Q {\ Displaystyle P \ Equiv Q}if #1084;#1086;#1078;#1085;#1086; #1087;#1086;#1083;#1091;#1095;#1080;#1090;#1100; #1080;#1079;, #1087;#1077;#1088;#1077;#1080;#1084;#1077;#1085;#1086;#1074;#1072;#1074; #1086;#1076;#1085;#1086; #1080;#1083;#1080; #1085;#1077;#1089;#1082;#1086;#1083;#1100;#1082;#1086; #1089;#1074;#1103;#1079;#1072;#1085;#1085;#1099;#1093; #1080;#1084;#1077;#1085; #1074;. Q {\ displaystyle Q} #1087; {\ displaystyle P} #1087; {\ displaystyle P}

#1040;#1082;#1089;#1080;#1086;#1084;#1099; #1087;#1072;#1088;#1072;#1083;#1083;#1077;#1083;#1100;#1085;#1086;#1081; #1082;#1086;#1084;#1087;#1086;#1079;#1080;#1094;#1080;#1080;:

  • #1087; | Q equiv; Q | #1087; {\ Displaystyle P | Q \ Equiv Q | P}
  • ( #1087; | Q ) | #1088; equiv; #1087; | ( Q | #1088; ) {\ Displaystyle (P | Q) | R \ #1101;#1082;#1074;#1080;#1074; P | (Q | R)}
  • #1087; | 0 equiv; #1087; {\ Displaystyle P | 0 \ #1101;#1082;#1074;#1080;#1074; P}

#1040;#1082;#1089;#1080;#1086;#1084;#1099; #1076;#1083;#1103; #1086;#1075;#1088;#1072;#1085;#1080;#1095;#1077;#1085;#1080;#1103;:

  • ( nu; #1048;#1082;#1089; ) ( nu; #1091; ) #1087; equiv; ( nu; #1091; ) ( nu; #1048;#1082;#1089; ) #1087; {\ Displaystyle (\ #1085;#1102; #1093;) (\ #1085;#1102; #1091;) #1087; \ #1101;#1082;#1074; (\ #1085;#1102; #1091;) (\ #1085;#1102; #1093;) #1087;}
  • ( nu; #1048;#1082;#1089; ) 0 equiv; 0 {\ Displaystyle (\ #1085;#1102; #1093;) 0 \ #1101;#1082;#1074;#1080;#1074; 0}

#1040;#1082;#1089;#1080;#1086;#1084;#1072; #1076;#1083;#1103; #1088;#1077;#1087;#1083;#1080;#1082;#1072;#1094;#1080;#1080;:

  • ! #1087; equiv; #1087; | ! #1087; {\ Displaystyle! P \ Equiv P |! P}

#1040;#1082;#1089;#1080;#1086;#1084;#1072;, #1089;#1074;#1103;#1079;#1099;#1074;#1072;#1102;#1097;#1072;#1103; #1086;#1075;#1088;#1072;#1085;#1080;#1095;#1077;#1085;#1080;#1077; #1080; #1087;#1072;#1088;#1072;#1083;#1083;#1077;#1083;#1100;:

  • ( nu; #1048;#1082;#1089; ) ( #1087; | Q ) equiv; ( nu; #1048;#1082;#1089; ) #1087; | Q {\ Displaystyle (\ #1085;#1102; #1093;) (#1087; | Q) \ #1101;#1082;#1074; (\ #1085;#1102; #1093;) #1087; | Q}#1077;#1089;#1083;#1080; x #1085;#1077; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1099;#1084; #1080;#1084;#1077;#1085;#1077;#1084;. Q {\ displaystyle Q}

#1069;#1090;#1072; #1087;#1086;#1089;#1083;#1077;#1076;#1085;#1103;#1103; #1072;#1082;#1089;#1080;#1086;#1084;#1072; #1080;#1079;#1074;#1077;#1089;#1090;#1085;#1072; #1082;#1072;#1082; #1072;#1082;#1089;#1080;#1086;#1084;#1072; laquo;#1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1103; #1086;#1073;#1083;#1072;#1089;#1090;#1080; #1074;#1080;#1076;#1080;#1084;#1086;#1089;#1090;#1080;raquo;. #1069;#1090;#1072; #1072;#1082;#1089;#1080;#1086;#1084;#1072; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1094;#1077;#1085;#1090;#1088;#1072;#1083;#1100;#1085;#1086;#1081;, #1087;#1086;#1089;#1082;#1086;#1083;#1100;#1082;#1091; #1086;#1085;#1072; #1086;#1087;#1080;#1089;#1099;#1074;#1072;#1077;#1090;, #1082;#1072;#1082; #1089;#1074;#1103;#1079;#1072;#1085;#1085;#1086;#1077; #1080;#1084;#1103; x #1084;#1086;#1078;#1077;#1090; #1073;#1099;#1090;#1100; #1074;#1099;#1090;#1077;#1089;#1085;#1077;#1085;#1086; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1077;#1084; #1074;#1099;#1074;#1086;#1076;#1072;, #1074;#1099;#1079;#1099;#1074;#1072;#1103; #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1077; #1086;#1073;#1083;#1072;#1089;#1090;#1080; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1103; x. #1042; #1090;#1077;#1093; #1089;#1083;#1091;#1095;#1072;#1103;#1093;, #1082;#1086;#1075;#1076;#1072; x #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1099;#1084; #1080;#1084;#1077;#1085;#1077;#1084;, #1084;#1086;#1078;#1077;#1090; #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1086;#1074;#1072;#1090;#1100;#1089;#1103; #1072;#1083;#1100;#1092;#1072;-#1087;#1088;#1077;#1086;#1073;#1088;#1072;#1079;#1086;#1074;#1072;#1085;#1080;#1077; #1076;#1083;#1103; #1087;#1088;#1086;#1076;#1086;#1083;#1078;#1077;#1085;#1080;#1103; #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1103;. Q {\ displaystyle Q}

#1057;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1072; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;

#1052;#1099; #1087;#1080;#1096;#1077;#1084;, #1077;#1089;#1083;#1080; #1084;#1086;#1078;#1077;#1090; #1074;#1099;#1087;#1086;#1083;#1085;#1080;#1090;#1100; #1096;#1072;#1075; #1074;#1099;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103;, #1087;#1086;#1089;#1083;#1077; #1082;#1086;#1090;#1086;#1088;#1086;#1075;#1086; #1086;#1085; #1089;#1077;#1081;#1095;#1072;#1089;. #1069;#1090;#1086; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1077; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1103;#1077;#1090;#1089;#1103; #1082;#1072;#1082; #1085;#1072;#1080;#1084;#1077;#1085;#1100;#1096;#1077;#1077; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1077;, #1079;#1072;#1084;#1082;#1085;#1091;#1090;#1086;#1077; #1087;#1086; #1085;#1072;#1073;#1086;#1088;#1091; #1087;#1088;#1072;#1074;#1080;#1083; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;. #1087; rarr; #1087; prime; {\ displaystyle P \ rightarrow P '} #1087; {\ displaystyle P} #1087; prime; {\ displaystyle P '} rarr; {\ displaystyle \ rightarrow}

#1054;#1089;#1085;#1086;#1074;#1085;#1086;#1077; #1087;#1088;#1072;#1074;#1080;#1083;#1086; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;, #1082;#1086;#1090;#1086;#1088;#1086;#1077; #1091;#1095;#1080;#1090;#1099;#1074;#1072;#1077;#1090; #1089;#1087;#1086;#1089;#1086;#1073;#1085;#1086;#1089;#1090;#1100; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1086;#1074; #1074;#1079;#1072;#1080;#1084;#1086;#1076;#1077;#1081;#1089;#1090;#1074;#1086;#1074;#1072;#1090;#1100; #1087;#1086; #1082;#1072;#1085;#1072;#1083;#1072;#1084;, #1089;#1083;#1077;#1076;#1091;#1102;#1097;#1077;#1077;:

  • #1048;#1082;#1089; macr; #10216; z #10217; . #1087; | #1048;#1082;#1089; ( #1091; ) . Q rarr; #1087; | Q [ z / #1091; ] {\ displaystyle {\ overline {x}} \ langle z \ rangle.P | x (y).Q \ rightarrow P | Q [z / y]}
#1075;#1076;#1077; #1086;#1073;#1086;#1079;#1085;#1072;#1095;#1072;#1077;#1090; #1087;#1088;#1086;#1094;#1077;#1089;#1089;, #1074; #1082;#1086;#1090;#1086;#1088;#1086;#1084; #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1086;#1077; #1080;#1084;#1103; #1073;#1099;#1083;#1086; #1079;#1072;#1084;#1077;#1085;#1077;#1085;#1086; #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1099;#1084;#1080; #1074;#1093;#1086;#1078;#1076;#1077;#1085;#1080;#1103;#1084;#1080;. #1045;#1089;#1083;#1080; #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1086;#1077; #1087;#1086;#1103;#1074;#1083;#1077;#1085;#1080;#1077; #1087;#1088;#1086;#1080;#1089;#1093;#1086;#1076;#1080;#1090; #1074; #1084;#1077;#1089;#1090;#1077;, #1075;#1076;#1077; #1086;#1085;#1086; #1085;#1077; #1073;#1099;#1083;#1086; #1073;#1099; #1073;#1077;#1089;#1087;#1083;#1072;#1090;#1085;#1099;#1084;, #1084;#1086;#1078;#1077;#1090; #1087;#1086;#1090;#1088;#1077;#1073;#1086;#1074;#1072;#1090;#1100;#1089;#1103; #1072;#1083;#1100;#1092;#1072;-#1087;#1088;#1077;#1086;#1073;#1088;#1072;#1079;#1086;#1074;#1072;#1085;#1080;#1077;. Q [ z / #1091; ] {\ Displaystyle Q [#1075; / #1091;]} Q {\ displaystyle Q} z {\ displaystyle z} #1091; {\ displaystyle y} #1091; {\ displaystyle y} z {\ displaystyle z}

#1045;#1089;#1090;#1100; #1090;#1088;#1080; #1076;#1086;#1087;#1086;#1083;#1085;#1080;#1090;#1077;#1083;#1100;#1085;#1099;#1093; #1087;#1088;#1072;#1074;#1080;#1083;#1072;:

  • #1045;#1089;#1083;#1080; #1090;#1086; #1090;#1086;#1078;#1077;. #1087; rarr; Q {\ displaystyle P \ rightarrow Q} #1087; | #1088; rarr; Q | #1088; {\ Displaystyle P | R \ rightarrow Q | R}
#1069;#1090;#1086; #1087;#1088;#1072;#1074;#1080;#1083;#1086; #1075;#1083;#1072;#1089;#1080;#1090;, #1095;#1090;#1086; #1087;#1072;#1088;#1072;#1083;#1083;#1077;#1083;#1100;#1085;#1072;#1103; #1082;#1086;#1084;#1087;#1086;#1079;#1080;#1094;#1080;#1103; #1085;#1077; #1087;#1088;#1077;#1087;#1103;#1090;#1089;#1090;#1074;#1091;#1077;#1090; #1074;#1099;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103;#1084;.
  • #1045;#1089;#1083;#1080;, #1090;#1086; #1090;#1086;#1078;#1077;. #1087; rarr; Q {\ displaystyle P \ rightarrow Q} ( nu; #1048;#1082;#1089; ) #1087; rarr; ( nu; #1048;#1082;#1089; ) Q {\ Displaystyle (\ #1085;#1102; #1093;) #1087; \ #1074;#1087;#1088;#1072;#1074;#1086; (\ #1085;#1102; #1093;) Q}
#1069;#1090;#1086; #1087;#1088;#1072;#1074;#1080;#1083;#1086; #1075;#1072;#1088;#1072;#1085;#1090;#1080;#1088;#1091;#1077;#1090;, #1095;#1090;#1086; #1074;#1099;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103; #1084;#1086;#1075;#1091;#1090; #1074;#1099;#1087;#1086;#1083;#1085;#1103;#1090;#1100;#1089;#1103; #1073;#1077;#1079; #1086;#1075;#1088;#1072;#1085;#1080;#1095;#1077;#1085;#1080;#1081;.
  • #1045;#1089;#1083;#1080; #1080; #1080;, #1090;#1086; #1078;#1077;. #1087; equiv; #1087; prime; {\ Displaystyle P \ Equiv P '} #1087; prime; rarr; Q prime; {\ displaystyle P '\ rightarrow Q'} Q prime; equiv; Q {\ Displaystyle Q '\ Equiv Q} #1087; rarr; Q {\ displaystyle P \ rightarrow Q}

#1055;#1086;#1089;#1083;#1077;#1076;#1085;#1077;#1077; #1087;#1088;#1072;#1074;#1080;#1083;#1086; #1075;#1083;#1072;#1089;#1080;#1090;, #1095;#1090;#1086; #1089;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1085;#1086; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1099;#1077; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1099; #1080;#1084;#1077;#1102;#1090; #1086;#1076;#1080;#1085;#1072;#1082;#1086;#1074;#1099;#1077; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;.

#1055;#1086;#1074;#1090;#1086;#1088;#1085;#1099;#1081; #1087;#1088;#1080;#1084;#1077;#1088;

#1056;#1072;#1089;#1089;#1084;#1086;#1090;#1088;#1080;#1084; #1077;#1097;#1077; #1088;#1072;#1079; #1087;#1088;#1086;#1094;#1077;#1089;#1089;

( nu; #1048;#1082;#1089; ) ( #1048;#1082;#1089; macr; #10216; z #10217; .0 | #1048;#1082;#1089; ( #1091; ) . #1091; macr; #10216; #1048;#1082;#1089; #10217; . #1048;#1082;#1089; ( #1091; ) .0 ) | z ( v ) . v macr; #10216; v #10217; .0 {\ displaystyle (\ nu x) ({\ overline {x}} \ langle z \ rangle.0 | x (y). {\ overline {y}} \ langle x \ rangle.x (y).0) | z (v). {\ overline {v}} \ langle v \ rangle.0}

#1055;#1088;#1080;#1084;#1077;#1085;#1103;#1103; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1077;#1085;#1080;#1077; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1080; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;, #1087;#1086;#1083;#1091;#1095;#1072;#1077;#1084; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1102;

( nu; #1048;#1082;#1089; ) ( #1048;#1082;#1089; macr; #10216; z #10217; .0 | #1048;#1082;#1089; ( #1091; ) . #1091; macr; #10216; #1048;#1082;#1089; #10217; . #1048;#1082;#1089; ( #1091; ) .0 ) | z ( v ) . v macr; #10216; v #10217; .0 rarr; ( nu; #1048;#1082;#1089; ) ( 0 | z macr; #10216; #1048;#1082;#1089; #10217; . #1048;#1082;#1089; ( #1091; ) .0 ) | z ( v ) . v macr; #10216; v #10217; .0 {\ displaystyle (\ nu x) ({\ overline {x}} \ langle z \ rangle.0 | x (y). {\ overline {y}} \ langle x \ rangle.x (y).0) | z (v). {\ overline {v}} \ langle v \ rangle.0 \ rightarrow (\ nu x) (0 | {\ overline {z}} \ langle x \ rangle.x (y).0) | z (v). {\ overline {v}} \ langle v \ rangle.0}

#1054;#1073;#1088;#1072;#1090;#1080;#1090;#1077; #1074;#1085;#1080;#1084;#1072;#1085;#1080;#1077;, #1082;#1072;#1082;, #1087;#1088;#1080;#1084;#1077;#1085;#1103;#1103; #1072;#1082;#1089;#1080;#1086;#1084;#1091; #1087;#1086;#1076;#1089;#1090;#1072;#1085;#1086;#1074;#1082;#1080; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;, #1089;#1074;#1086;#1073;#1086;#1076;#1085;#1099;#1077; #1074;#1093;#1086;#1078;#1076;#1077;#1085;#1080;#1103; #1090;#1077;#1087;#1077;#1088;#1100; #1087;#1086;#1084;#1077;#1095;#1077;#1085;#1099; #1082;#1072;#1082;. #1091; {\ displaystyle y} z {\ displaystyle z}

#1044;#1072;#1083;#1077;#1077; #1087;#1086;#1083;#1091;#1095;#1072;#1077;#1084; #1089;#1086;#1082;#1088;#1072;#1097;#1077;#1085;#1080;#1077;

( nu; #1048;#1082;#1089; ) ( 0 | z macr; #10216; #1048;#1082;#1089; #10217; . #1048;#1082;#1089; ( #1091; ) .0 ) | z ( v ) . v macr; #10216; v #10217; .0 rarr; ( nu; #1048;#1082;#1089; ) ( 0 | #1048;#1082;#1089; ( #1091; ) .0 | #1048;#1082;#1089; macr; #10216; #1048;#1082;#1089; #10217; .0 ) {\ displaystyle (\ nu x) (0 | {\ overline {z}} \ langle x \ rangle.x (y).0) | z (v). {\ overline {v}} \ langle v \ rangle. 0 \ rightarrow (\ nu x) (0 | x (y).0 | {\ overline {x}} \ langle x \ rangle.0)}

#1054;#1073;#1088;#1072;#1090;#1080;#1090;#1077; #1074;#1085;#1080;#1084;#1072;#1085;#1080;#1077;, #1095;#1090;#1086;, #1087;#1086;#1089;#1082;#1086;#1083;#1100;#1082;#1091; #1083;#1086;#1082;#1072;#1083;#1100;#1085;#1086;#1077; #1080;#1084;#1103; x #1073;#1099;#1083;#1086; #1074;#1099;#1074;#1077;#1076;#1077;#1085;#1086;, #1086;#1073;#1083;#1072;#1089;#1090;#1100; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1103; x #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1072;, #1095;#1090;#1086;#1073;#1099; #1086;#1093;#1074;#1072;#1090;#1080;#1090;#1100; #1090;#1072;#1082;#1078;#1077; #1090;#1088;#1077;#1090;#1080;#1081; #1082;#1086;#1084;#1087;#1086;#1085;#1077;#1085;#1090;. #1069;#1090;#1086; #1073;#1099;#1083;#1086; #1079;#1072;#1092;#1080;#1082;#1089;#1080;#1088;#1086;#1074;#1072;#1085;#1086; #1089; #1087;#1086;#1084;#1086;#1097;#1100;#1102; #1072;#1082;#1089;#1080;#1086;#1084;#1099; #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1103; #1086;#1073;#1083;#1072;#1089;#1090;#1080; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1103;.

#1044;#1072;#1083;#1077;#1077;, #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1091;#1103; #1072;#1082;#1089;#1080;#1086;#1084;#1091; #1087;#1086;#1076;#1089;#1090;#1072;#1085;#1086;#1074;#1082;#1080; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;, #1087;#1086;#1083;#1091;#1095;#1072;#1077;#1084;

( nu; #1048;#1082;#1089; ) ( 0 | 0 | 0 ) {\ Displaystyle (\ #1085;#1102; #1093;) (0 | 0 | 0)}

#1053;#1072;#1082;#1086;#1085;#1077;#1094;, #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1091;#1103; #1072;#1082;#1089;#1080;#1086;#1084;#1099; #1087;#1072;#1088;#1072;#1083;#1083;#1077;#1083;#1100;#1085;#1086;#1081; #1082;#1086;#1084;#1087;#1086;#1079;#1080;#1094;#1080;#1080; #1080; #1086;#1075;#1088;#1072;#1085;#1080;#1095;#1077;#1085;#1080;#1103;, #1087;#1086;#1083;#1091;#1095;#1072;#1077;#1084;

0 {\ displaystyle 0}

#1055;#1086;#1084;#1077;#1095;#1077;#1085;#1085;#1072;#1103; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1072;

#1042; #1082;#1072;#1095;#1077;#1089;#1090;#1074;#1077; #1072;#1083;#1100;#1090;#1077;#1088;#1085;#1072;#1090;#1080;#1074;#1099;, #1084;#1086;#1078;#1085;#1086; #1087;#1088;#1080;#1076;#1072;#1090;#1100; #1087;#1080;-#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1102; #1087;#1086;#1084;#1077;#1095;#1077;#1085;#1085;#1091;#1102; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1091; #1087;#1077;#1088;#1077;#1093;#1086;#1076;#1072; (#1082;#1072;#1082; #1101;#1090;#1086; #1073;#1099;#1083;#1086; #1089;#1076;#1077;#1083;#1072;#1085;#1086; #1089; #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077;#1084; #1082;#1086;#1084;#1084;#1091;#1085;#1080;#1082;#1072;#1094;#1080;#1086;#1085;#1085;#1099;#1093; #1089;#1080;#1089;#1090;#1077;#1084; ). #1042; #1101;#1090;#1086;#1081; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1077; #1087;#1077;#1088;#1077;#1093;#1086;#1076; #1080;#1079; #1086;#1076;#1085;#1086;#1075;#1086; #1089;#1086;#1089;#1090;#1086;#1103;#1085;#1080;#1103; #1074; #1076;#1088;#1091;#1075;#1086;#1077; #1087;#1086;#1089;#1083;#1077; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1103; #1086;#1073;#1086;#1079;#1085;#1072;#1095;#1072;#1077;#1090;#1089;#1103; #1082;#1072;#1082;: #1087; {\ displaystyle P} #1087; prime; {\ displaystyle P '} alpha; {\ displaystyle \ alpha}

  • #1087; rarr; alpha; #1087; prime; {\ Displaystyle P \, {\ xrightarrow {\ overset {} {\ alpha}}} P '}

#1043;#1076;#1077; #1089;#1086;#1089;#1090;#1086;#1103;#1085;#1080;#1103; #1080; #1087;#1088;#1077;#1076;#1089;#1090;#1072;#1074;#1083;#1103;#1102;#1090; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1099; #1080; #1103;#1074;#1083;#1103;#1102;#1090;#1089;#1103; #1083;#1080;#1073;#1086; #1074;#1093;#1086;#1076;#1085;#1099;#1084; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1077;#1084;, #1074;#1099;#1093;#1086;#1076;#1085;#1099;#1084; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1077;#1084;, #1083;#1080;#1073;#1086; #1084;#1086;#1083;#1095;#1072;#1083;#1080;#1074;#1099;#1084; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1077;#1084; tau;. #1087; {\ displaystyle P} #1087; prime; {\ displaystyle P '} alpha; {\ displaystyle \ alpha} #1072; ( #1048;#1082;#1089; ) {\ Displaystyle #1072; (#1093;)} #1072; macr; #10216; #1048;#1082;#1089; #10217; {\ displaystyle {\ overline {a}} \ langle x \ rangle}

#1057;#1090;#1072;#1085;#1076;#1072;#1088;#1090;#1085;#1099;#1081; #1088;#1077;#1079;#1091;#1083;#1100;#1090;#1072;#1090; #1074; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1080; #1087;#1086;#1084;#1077;#1095;#1077;#1085;#1085;#1086;#1081; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1080; #1089;#1086;#1089;#1090;#1086;#1080;#1090; #1074; #1090;#1086;#1084;, #1095;#1090;#1086; #1086;#1085;#1072; #1089;#1086;#1075;#1083;#1072;#1089;#1091;#1077;#1090;#1089;#1103; #1089; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1086;#1081; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080; #1076;#1086; #1089;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1085;#1086;#1081; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1086;#1089;#1090;#1080; #1074; #1090;#1086;#1084; #1089;#1084;#1099;#1089;#1083;#1077;, #1095;#1090;#1086; #1090;#1086;#1075;#1076;#1072; #1080; #1090;#1086;#1083;#1100;#1082;#1086; #1090;#1086;#1075;#1076;#1072;, #1082;#1086;#1075;#1076;#1072; #1087; rarr; #1087; prime; {\ displaystyle P \ rightarrow P '} #1087; rarr; tau; equiv; #1087; prime; {\ Displaystyle P \, \ xrightarrow {\ overset {} {\ tau}} \ Equiv P '}

#1056;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1103; #1080; #1074;#1072;#1088;#1080;#1072;#1085;#1090;#1099;

#1055;#1088;#1080;#1074;#1077;#1076;#1077;#1085;#1085;#1099;#1081; #1074;#1099;#1096;#1077; #1089;#1080;#1085;#1090;#1072;#1082;#1089;#1080;#1089; #1084;#1080;#1085;#1080;#1084;#1072;#1083;#1077;#1085;. #1054;#1076;#1085;#1072;#1082;#1086; #1089;#1080;#1085;#1090;#1072;#1082;#1089;#1080;#1089; #1084;#1086;#1078;#1085;#1086; #1080;#1079;#1084;#1077;#1085;#1103;#1090;#1100; #1087;#1086;-#1088;#1072;#1079;#1085;#1086;#1084;#1091;.

#1053;#1077;#1076;#1077;#1090;#1077;#1088;#1084;#1080;#1085;#1080;#1088;#1086;#1074;#1072;#1085; #1086;#1087;#1077;#1088;#1072;#1090;#1086;#1088; #1074;#1099;#1073;#1086;#1088;#1072; #1084;#1086;#1078;#1077;#1090; #1073;#1099;#1090;#1100; #1076;#1086;#1073;#1072;#1074;#1083;#1077;#1085; #1082; #1089;#1080;#1085;#1090;#1072;#1082;#1089;#1080;#1089;#1091;. #1087; + Q {\ displaystyle P + Q}

#1042; #1089;#1080;#1085;#1090;#1072;#1082;#1089;#1080;#1089; #1084;#1086;#1078;#1085;#1086; #1076;#1086;#1073;#1072;#1074;#1080;#1090;#1100; #1087;#1088;#1086;#1074;#1077;#1088;#1082;#1091; #1085;#1072; #1088;#1072;#1074;#1077;#1085;#1089;#1090;#1074;#1086; #1080;#1084;#1077;#1085;. #1069;#1090;#1086;#1090; #1086;#1087;#1077;#1088;#1072;#1090;#1086;#1088; #1089;#1086;#1087;#1086;#1089;#1090;#1072;#1074;#1083;#1077;#1085;#1080;#1103; #1084;#1086;#1078;#1077;#1090; #1076;#1077;#1081;#1089;#1090;#1074;#1086;#1074;#1072;#1090;#1100; #1090;#1072;#1082;, #1082;#1072;#1082; #1077;#1089;#1083;#1080; #1073;#1099; #1080; #1090;#1086;#1083;#1100;#1082;#1086; #1077;#1089;#1083;#1080; x #1080; #1089;#1086;#1074;#1087;#1072;#1076;#1072;#1083;#1080; #1089; #1080;#1084;#1077;#1085;#1072;#1084;#1080;. #1058;#1086;#1095;#1085;#1086; #1090;#1072;#1082; #1078;#1077; #1084;#1086;#1078;#1085;#1086; #1076;#1086;#1073;#1072;#1074;#1080;#1090;#1100; #1086;#1087;#1077;#1088;#1072;#1090;#1086;#1088; #1085;#1077;#1089;#1086;#1074;#1087;#1072;#1076;#1077;#1085;#1080;#1103; #1076;#1083;#1103; #1085;#1077;#1088;#1072;#1074;#1077;#1085;#1089;#1090;#1074;#1072; #1080;#1084;#1077;#1085;. #1055;#1088;#1072;#1082;#1090;#1080;#1095;#1077;#1089;#1082;#1080;#1077; #1087;#1088;#1086;#1075;#1088;#1072;#1084;#1084;#1099;, #1082;#1086;#1090;#1086;#1088;#1099;#1077; #1084;#1086;#1075;#1091;#1090; #1087;#1077;#1088;#1077;#1076;#1072;#1074;#1072;#1090;#1100; #1080;#1084;#1077;#1085;#1072; (URL-#1072;#1076;#1088;#1077;#1089;#1072; #1080;#1083;#1080; #1091;#1082;#1072;#1079;#1072;#1090;#1077;#1083;#1080;), #1095;#1072;#1089;#1090;#1086; #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1091;#1102;#1090; #1090;#1072;#1082;#1091;#1102; #8203;#8203;#1092;#1091;#1085;#1082;#1094;#1080;#1086;#1085;#1072;#1083;#1100;#1085;#1086;#1089;#1090;#1100;: #1076;#1083;#1103; #1087;#1088;#1103;#1084;#1086;#1075;#1086; #1084;#1086;#1076;#1077;#1083;#1080;#1088;#1086;#1074;#1072;#1085;#1080;#1103; #1090;#1072;#1082;#1086;#1081; #1092;#1091;#1085;#1082;#1094;#1080;#1086;#1085;#1072;#1083;#1100;#1085;#1086;#1089;#1090;#1080; #1074;#1085;#1091;#1090;#1088;#1080; #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103; #1095;#1072;#1089;#1090;#1086; #1073;#1099;#1074;#1072;#1077;#1090; #1087;#1086;#1083;#1077;#1079;#1085;#1086; #1101;#1090;#1086; #1080; #1089;#1074;#1103;#1079;#1072;#1085;#1085;#1099;#1077; #1089; #1085;#1080;#1084; #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1103;. [ #1048;#1082;#1089; #1079;#1085;#1072;#1082; #1088;#1072;#1074;#1085;#1086; #1091; ] #1087; {\ displaystyle [x = y] P} #1087; {\ displaystyle P} #1091; {\ displaystyle y}

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#1048;#1082;#1089; macr; #10216; #1091; 1 , #8943; , #1091; #1087; #10217; . #1087; {\ displaystyle {\ overline {x}} \ langle y_ {1}, \ cdots, y_ {n} \ rangle.P} #1082;#1086;#1076;#1080;#1088;#1091;#1077;#1090;#1089;#1103; #1082;#1072;#1082; ( nu; #1096; ) #1048;#1082;#1089; macr; #10216; #1096; #10217; . #1096; macr; #10216; #1091; 1 #10217; . #8943; . #1096; macr; #10216; #1091; #1087; #10217; . [ #1087; ] {\ displaystyle (\ nu w) {\ overline {x}} \ langle w \ rangle. {\ overline {w}} \ langle y_ {1} \ rangle. \ cdots. {\ overline {w}} \ langle y_ {n} \ rangle. [P]}

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#1057;#1084;. #1058;#1072;#1082;#1078;#1077;: #1041;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1103;

#1063;#1090;#1086; #1082;#1072;#1089;#1072;#1077;#1090;#1089;#1103; #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1081; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1086;#1074;, pi; -#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077; #1087;#1086;#1079;#1074;#1086;#1083;#1103;#1077;#1090; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1080;#1090;#1100; #1101;#1082;#1074;#1080;#1074;#1072;#1083;#1077;#1085;#1090;#1085;#1086;#1089;#1090;#1100; #1073;#1080;#1084;#1086;#1076;#1077;#1083;#1080;#1088;#1086;#1074;#1072;#1085;#1080;#1103;. #1042; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1080; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1077;#1085;#1080;#1077; #1101;#1082;#1074;#1080;#1074;#1072;#1083;#1077;#1085;#1090;#1085;#1086;#1089;#1090;#1080; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1080; (#1090;#1072;#1082;#1078;#1077; #1080;#1079;#1074;#1077;#1089;#1090;#1085;#1086;#1081; #1082;#1072;#1082; #1073;#1080;#1089;#1093;#1086;#1078;#1077;#1089;#1090;#1100;) #1084;#1086;#1078;#1077;#1090; #1073;#1099;#1090;#1100; #1086;#1089;#1085;#1086;#1074;#1072;#1085;#1086; #1083;#1080;#1073;#1086; #1085;#1072; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1077; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;, #1083;#1080;#1073;#1086; #1085;#1072; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1077; #1087;#1086;#1084;#1077;#1095;#1077;#1085;#1085;#1086;#1075;#1086; #1087;#1077;#1088;#1077;#1093;#1086;#1076;#1072;.

#1057;#1091;#1097;#1077;#1089;#1090;#1074;#1091;#1077;#1090; (#1087;#1086; #1082;#1088;#1072;#1081;#1085;#1077;#1081; #1084;#1077;#1088;#1077;) #1090;#1088;#1080; #1088;#1072;#1079;#1083;#1080;#1095;#1085;#1099;#1093; #1089;#1087;#1086;#1089;#1086;#1073;#1072; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1077;#1085;#1080;#1103; #1084;#1077;#1095;#1077;#1085;#1086;#1081; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1086;#1085;#1085;#1086;#1081; #1101;#1082;#1074;#1080;#1074;#1072;#1083;#1077;#1085;#1090;#1085;#1086;#1089;#1090;#1080; #1074; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1080;: #1088;#1072;#1085;#1085;#1077;#1077;, #1087;#1086;#1079;#1076;#1085;#1077;#1077; #1080; #1086;#1090;#1082;#1088;#1099;#1090;#1086;#1077; #1076;#1074;#1091;#1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086;. #1069;#1090;#1086; #1087;#1088;#1086;#1080;#1089;#1090;#1077;#1082;#1072;#1077;#1090; #1080;#1079; #1090;#1086;#1075;#1086; #1092;#1072;#1082;#1090;#1072;, #1095;#1090;#1086; pi; -#1074;#1099;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077;#1084; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072; #1087;#1077;#1088;#1077;#1076;#1072;#1095;#1080; #1079;#1085;#1072;#1095;#1077;#1085;#1080;#1081;.

#1042; #1086;#1089;#1090;#1072;#1074;#1096;#1077;#1081;#1089;#1103; #1095;#1072;#1089;#1090;#1080; #1101;#1090;#1086;#1075;#1086; #1088;#1072;#1079;#1076;#1077;#1083;#1072; #1084;#1099; #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1091;#1077;#1084; #1080; #1086;#1073;#1086;#1079;#1085;#1072;#1095;#1072;#1077;#1084; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1099; #1080; #1086;#1073;#1086;#1079;#1085;#1072;#1095;#1072;#1077;#1084; #1073;#1080;#1085;#1072;#1088;#1085;#1099;#1077; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1103; #1085;#1072;#1076; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072;#1084;#1080;. #1087; {\ displaystyle p} q {\ displaystyle q} #1088; {\ displaystyle R}

#1056;#1072;#1085;#1085;#1077;#1077; #1080; #1087;#1086;#1079;#1076;#1085;#1077;#1077; #1076;#1074;#1086;#1081;#1085;#1086;#1077; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086;

#1048; #1088;#1072;#1085;#1085;#1077;#1077;, #1080; #1087;#1086;#1079;#1076;#1085;#1077;#1077; #1076;#1074;#1086;#1081;#1085;#1086;#1077; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086; #1073;#1099;#1083;#1080; #1089;#1092;#1086;#1088;#1084;#1091;#1083;#1080;#1088;#1086;#1074;#1072;#1085;#1099; #1052;#1080;#1083;#1085;#1077;#1088;#1086;#1084;, #1055;#1072;#1088;#1088;#1086;#1091; #1080; #1059;#1086;#1082;#1077;#1088;#1086;#1084; #1074; #1080;#1093; #1086;#1088;#1080;#1075;#1080;#1085;#1072;#1083;#1100;#1085;#1086;#1081; #1089;#1090;#1072;#1090;#1100;#1077; #1086; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1080;.

#1041;#1080;#1085;#1072;#1088;#1085;#1086;#1077; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1077; #1085;#1072;#1076; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072;#1084;#1080; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1088;#1072;#1085;#1085;#1077;#1081; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1077;#1081;, #1077;#1089;#1083;#1080; #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1081; #1087;#1072;#1088;#1099; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1086;#1074;, #1088; {\ displaystyle R} ( #1087; , q ) isin; #1088; {\ displaystyle (p, q) \ in R}

  • #1074;#1089;#1103;#1082;#1080;#1081; #1088;#1072;#1079;, #1082;#1086;#1075;#1076;#1072; #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1075;#1086; #1080;#1084;#1077;#1085;#1080; #1089;#1091;#1097;#1077;#1089;#1090;#1074;#1091;#1077;#1090; #1090;#1072;#1082;#1086;#1077;, #1095;#1090;#1086; #1080; ; #1087; rarr; #1072; ( #1048;#1082;#1089; ) #1087; prime; {\ displaystyle p \, {\ xrightarrow {a (x)}} \, p '} #1091; {\ displaystyle y} q prime; {\ displaystyle q '} q rarr; #1072; ( #1048;#1082;#1089; ) q prime; {\ Displaystyle #1076; \, {\ xrightarrow {#1072; (#1093;)}} \, #1076; '} ( #1087; prime; [ #1091; / #1048;#1082;#1089; ] , q prime; [ #1091; / #1048;#1082;#1089; ] ) isin; #1088; {\ Displaystyle (#1087; '[#1091; / #1093;], #1076;' [#1091; / #1093;]) \ #1074; R}
  • #1076;#1083;#1103; #1083;#1102;#1073;#1086;#1075;#1086; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1103;, #1085;#1077; #1103;#1074;#1083;#1103;#1102;#1097;#1077;#1075;#1086;#1089;#1103; #1074;#1093;#1086;#1076;#1086;#1084;, #1077;#1089;#1083;#1080; #1090;#1086;#1075;#1076;#1072; #1089;#1091;#1097;#1077;#1089;#1090;#1074;#1091;#1077;#1090; #1090;#1072;#1082;#1086;#1077;, #1095;#1090;#1086; #1080; ; alpha; {\ displaystyle \ alpha} #1087; rarr; alpha; #1087; prime; {\ displaystyle {p {\ xrightarrow {\ overset {} {\ alpha}}} p '}} q prime; {\ displaystyle q '} q rarr; alpha; q prime; {\ displaystyle q {\ xrightarrow {\ overset {} {\ alpha}}} q '} ( #1087; prime; , q prime; ) isin; #1088; {\ displaystyle (p ', q') \ in R}
  • #1080; #1090;#1088;#1077;#1073;#1086;#1074;#1072;#1085;#1080;#1103; #1089;#1080;#1084;#1084;#1077;#1090;#1088;#1080;#1095;#1085;#1099; #1080; #1074;#1079;#1072;#1080;#1084;#1086;#1079;#1072;#1084;#1077;#1085;#1103;#1077;#1084;#1099;. #1087; {\ displaystyle p} q {\ displaystyle q}

#1055;#1088;#1086;#1094;#1077;#1089;#1089;#1099; #1080;, #1082;#1072;#1082; #1075;#1086;#1074;#1086;#1088;#1103;#1090;, #1103;#1074;#1083;#1103;#1102;#1090;#1089;#1103; #1088;#1072;#1085;#1085;#1080;#1084;#1080; #1073;#1080;#1089;#1080;#1084;#1080;#1083;#1103;#1088;#1072;#1084;#1080;, #1077;#1089;#1083;#1080; #1087;#1072;#1088;#1072; #1079;#1072;#1087;#1080;#1089;#1099;#1074;#1072;#1077;#1090;#1089;#1103; #1076;#1083;#1103; #1085;#1077;#1082;#1086;#1090;#1086;#1088;#1086;#1081; #1088;#1072;#1085;#1085;#1077;#1081; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1080;. #1087; {\ displaystyle p} q {\ displaystyle q} #1087; sim; #1077; q {\ displaystyle p \ sim _ {e} q} ( #1087; , q ) isin; #1088; {\ displaystyle (p, q) \ in R} #1088; {\ displaystyle R}

#1055;#1088;#1080; #1087;#1086;#1079;#1076;#1085;#1077;#1084; #1076;#1074;#1086;#1081;#1085;#1086;#1084; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1077; #1087;#1077;#1088;#1077;#1093;#1086;#1076;#1085;#1086;#1077; #1089;#1086;#1074;#1087;#1072;#1076;#1077;#1085;#1080;#1077; #1085;#1077; #1076;#1086;#1083;#1078;#1085;#1086; #1079;#1072;#1074;#1080;#1089;#1077;#1090;#1100; #1086;#1090; #1087;#1077;#1088;#1077;#1076;#1072;#1074;#1072;#1077;#1084;#1086;#1075;#1086; #1080;#1084;#1077;#1085;#1080;. #1041;#1080;#1085;#1072;#1088;#1085;#1086;#1077; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1077; #1085;#1072;#1076; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072;#1084;#1080; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1087;#1086;#1079;#1076;#1085;#1077;#1081; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1077;#1081;, #1077;#1089;#1083;#1080; #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1081; #1087;#1072;#1088;#1099; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1086;#1074;, #1088; {\ displaystyle R} ( #1087; , q ) isin; #1088; {\ displaystyle (p, q) \ in R}

  • #1074;#1089;#1103;#1082;#1080;#1081; #1088;#1072;#1079;, #1082;#1086;#1075;#1076;#1072; #1076;#1083;#1103; #1085;#1077;#1082;#1086;#1090;#1086;#1088;#1099;#1093; #1101;#1090;#1086; #1074;#1099;#1087;#1086;#1083;#1085;#1103;#1077;#1090;#1089;#1103; #1080; #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1075;#1086; #1080;#1084;#1077;#1085;#1080; y ; #1087; rarr; #1072; ( #1048;#1082;#1089; ) #1087; prime; {\ Displaystyle #1088; {\ xrightarrow {#1072; (#1093;)}} #1088; '} q prime; {\ displaystyle q '} q rarr; #1072; ( #1048;#1082;#1089; ) q prime; {\ Displaystyle #1076; {\ xrightarrow {#1072; (#1093;)}} #1076; '} ( #1087; prime; [ #1091; / #1048;#1082;#1089; ] , q prime; [ #1091; / #1048;#1082;#1089; ] ) isin; #1088; {\ Displaystyle (#1087; '[#1091; / #1093;], #1076;' [#1091; / #1093;]) \ #1074; R}
  • #1076;#1083;#1103; #1083;#1102;#1073;#1086;#1075;#1086; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1103;, #1085;#1077; #1103;#1074;#1083;#1103;#1102;#1097;#1077;#1075;#1086;#1089;#1103; #1074;#1093;#1086;#1076;#1086;#1084;, #1077;#1089;#1083;#1080; #1087;#1086;#1076;#1088;#1072;#1079;#1091;#1084;#1077;#1074;#1072;#1077;#1090;, #1095;#1090;#1086; #1089;#1091;#1097;#1077;#1089;#1090;#1074;#1091;#1077;#1090; #1090;#1072;#1082;#1086;#1077;, #1095;#1090;#1086; #1080; ; alpha; {\ displaystyle \ alpha} #1087; rarr; alpha; #1087; prime; {\ displaystyle p {\ xrightarrow {\ overset {} {\ alpha}}} p '} q prime; {\ displaystyle q '} q rarr; alpha; q prime; {\ displaystyle q {\ xrightarrow {\ overset {} {\ alpha}}} q '} ( #1087; prime; , q prime; ) isin; #1088; {\ displaystyle (p ', q') \ in R}
  • #1080; #1090;#1088;#1077;#1073;#1086;#1074;#1072;#1085;#1080;#1103; #1089;#1080;#1084;#1084;#1077;#1090;#1088;#1080;#1095;#1085;#1099; #1080; #1074;#1079;#1072;#1080;#1084;#1086;#1079;#1072;#1084;#1077;#1085;#1103;#1077;#1084;#1099;. #1087; {\ displaystyle p} q {\ displaystyle q}

#1055;#1088;#1086;#1094;#1077;#1089;#1089;#1099; #1080;, #1082;#1072;#1082; #1075;#1086;#1074;#1086;#1088;#1103;#1090;, #1103;#1074;#1083;#1103;#1102;#1090;#1089;#1103; #1087;#1086;#1079;#1076;#1085;#1080;#1084;#1080; #1073;#1080;#1089;#1080;#1084;#1080;#1083;#1103;#1088;#1072;#1084;#1080;, #1077;#1089;#1083;#1080; #1087;#1072;#1088;#1072; #1079;#1072;#1087;#1080;#1089;#1099;#1074;#1072;#1077;#1090;#1089;#1103; #1076;#1083;#1103; #1085;#1077;#1082;#1086;#1090;#1086;#1088;#1086;#1081; #1087;#1086;#1079;#1076;#1085;#1077;#1081; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1080;. #1087; {\ displaystyle p} q {\ displaystyle q} #1087; sim; #1083; q {\ displaystyle p \ sim _ {l} q} ( #1087; , q ) isin; #1088; {\ displaystyle (p, q) \ in R} #1088; {\ displaystyle R}

#1054;#1073;#1072; #1080; #1089;#1090;#1088;#1072;#1076;#1072;#1102;#1090; #1086;#1090; #1087;#1088;#1086;#1073;#1083;#1077;#1084;#1099;, #1079;#1072;#1082;#1083;#1102;#1095;#1072;#1102;#1097;#1077;#1081;#1089;#1103; #1074; #1090;#1086;#1084;, #1095;#1090;#1086; #1086;#1085;#1080; #1085;#1077; #1103;#1074;#1083;#1103;#1102;#1090;#1089;#1103; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1103;#1084;#1080; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1086;#1089;#1090;#1080; #1074; #1090;#1086;#1084; #1089;#1084;#1099;#1089;#1083;#1077;, #1095;#1090;#1086; #1086;#1085;#1080; #1085;#1077; #1089;#1086;#1093;#1088;#1072;#1085;#1103;#1102;#1090;#1089;#1103; #1074;#1089;#1077;#1084;#1080; #1082;#1086;#1085;#1089;#1090;#1088;#1091;#1082;#1094;#1080;#1103;#1084;#1080; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072;. #1058;#1086;#1095;#1085;#1077;#1077;, #1089;#1091;#1097;#1077;#1089;#1090;#1074;#1091;#1102;#1090; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1099; #1080; #1090;#1072;#1082;#1080;#1077;, #1095;#1090;#1086; #1085;#1086;. #1069;#1090;#1091; #1087;#1088;#1086;#1073;#1083;#1077;#1084;#1091; #1084;#1086;#1078;#1085;#1086; #1088;#1077;#1096;#1080;#1090;#1100;, #1088;#1072;#1089;#1089;#1084;#1072;#1090;#1088;#1080;#1074;#1072;#1103; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1103; #1084;#1072;#1082;#1089;#1080;#1084;#1072;#1083;#1100;#1085;#1086;#1081; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1086;#1089;#1090;#1080;, #1074;#1082;#1083;#1102;#1095;#1077;#1085;#1085;#1099;#1077; #1074; #1080;, #1080;#1079;#1074;#1077;#1089;#1090;#1085;#1099;#1077; #1082;#1072;#1082; #1088;#1072;#1085;#1085;#1103;#1103; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1086;#1089;#1090;#1100; #1080; #1087;#1086;#1079;#1076;#1085;#1103;#1103; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1086;#1089;#1090;#1100;, #1089;#1086;#1086;#1090;#1074;#1077;#1090;#1089;#1090;#1074;#1077;#1085;#1085;#1086;. sim; #1077; {\ displaystyle \ sim _ {e}} sim; #1083; {\ displaystyle \ sim _ {l}} #1087; {\ displaystyle p} q {\ displaystyle q} #1087; sim; #1077; q {\ displaystyle p \ sim _ {e} q} #1072; ( #1048;#1082;#1089; ) . #1087; #8769; #1077; #1072; ( #1048;#1082;#1089; ) . q {\ Displaystyle #1072; (#1093;).p \ not \ sim _ {#1077;} #1072; (#1093;).q} sim; #1077; {\ displaystyle \ sim _ {e}} sim; #1083; {\ displaystyle \ sim _ {l}}

#1054;#1090;#1082;#1088;#1099;#1090;#1086;#1077; #1076;#1074;#1086;#1081;#1085;#1086;#1077; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086;

#1050; #1089;#1095;#1072;#1089;#1090;#1100;#1102;, #1074;#1086;#1079;#1084;#1086;#1078;#1085;#1086; #1090;#1088;#1077;#1090;#1100;#1077; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1077;#1085;#1080;#1077;, #1082;#1086;#1090;#1086;#1088;#1086;#1077; #1087;#1086;#1079;#1074;#1086;#1083;#1103;#1077;#1090; #1080;#1079;#1073;#1077;#1078;#1072;#1090;#1100; #1101;#1090;#1086;#1081; #1087;#1088;#1086;#1073;#1083;#1077;#1084;#1099;, #1072; #1080;#1084;#1077;#1085;#1085;#1086; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1077;#1085;#1080;#1077; #1086;#1090;#1082;#1088;#1099;#1090;#1086;#1075;#1086; #1076;#1074;#1086;#1081;#1085;#1086;#1075;#1086; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1072;, #1073;#1083;#1072;#1075;#1086;#1076;#1072;#1088;#1103; #1057;#1072;#1085;#1076;#1078;#1086;#1088;#1076;#1078;#1080;.

#1041;#1080;#1085;#1072;#1088;#1085;#1086;#1077; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1077; #1085;#1072;#1076; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072;#1084;#1080; - #1101;#1090;#1086; #1086;#1090;#1082;#1088;#1099;#1090;#1072;#1103; #1076;#1074;#1086;#1081;#1085;#1072;#1103; #1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1103;, #1077;#1089;#1083;#1080; #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1081; #1087;#1072;#1088;#1099; #1101;#1083;#1077;#1084;#1077;#1085;#1090;#1086;#1074; #1080; #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1081; #1087;#1086;#1076;#1089;#1090;#1072;#1085;#1086;#1074;#1082;#1080; #1080;#1084;#1077;#1085;#1080; #1080; #1082;#1072;#1078;#1076;#1086;#1075;#1086; #1076;#1077;#1081;#1089;#1090;#1074;#1080;#1103; #1074;#1089;#1103;#1082;#1080;#1081; #1088;#1072;#1079;, #1082;#1086;#1075;#1076;#1072; #1090;#1086;#1075;#1076;#1072; #1089;#1091;#1097;#1077;#1089;#1090;#1074;#1091;#1102;#1090; #1090;#1072;#1082;#1080;#1077;, #1095;#1090;#1086; #1080;. #1088; {\ displaystyle R} ( #1087; , q ) isin; #1088; {\ displaystyle (p, q) \ in R} sigma; {\ displaystyle \ sigma} alpha; {\ displaystyle \ alpha} #1087; sigma; rarr; alpha; #1087; prime; {\ displaystyle p \ sigma {\ xrightarrow {\ overset {} {\ alpha}}} p '} q prime; {\ displaystyle q '} q sigma; rarr; alpha; q prime; {\ displaystyle q \ sigma {\ xrightarrow {\ overset {} {\ alpha}}} q '} ( #1087; prime; , q prime; ) isin; #1088; {\ displaystyle (p ', q') \ in R}

#1055;#1088;#1086;#1094;#1077;#1089;#1089;#1099; #1080; #1085;#1072;#1079;#1099;#1074;#1072;#1102;#1090;#1089;#1103; #1086;#1090;#1082;#1088;#1099;#1090;#1099;#1084;#1080; #1073;#1080;#1089;#1080;#1084;#1080;#1083;#1103;#1088;#1072;#1084;#1080;, #1077;#1089;#1083;#1080; #1086;#1085;#1080; #1079;#1072;#1087;#1080;#1089;#1099;#1074;#1072;#1102;#1090;#1089;#1103; #1074; #1087;#1072;#1088;#1091; #1076;#1083;#1103; #1085;#1077;#1082;#1086;#1090;#1086;#1088;#1086;#1081; #1086;#1090;#1082;#1088;#1099;#1090;#1086;#1081; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1080;. #1087; {\ displaystyle p} q {\ displaystyle q} #1087; sim; #1086; q {\ displaystyle p \ sim _ {o} q} ( #1087; , q ) isin; #1088; {\ displaystyle (p, q) \ in R} #1088; {\ displaystyle R}

#1056;#1072;#1079;#1083;#1080;#1095;#1072;#1102;#1090; #1088;#1072;#1085;#1085;#1077;#1077;, #1087;#1086;#1079;#1076;#1085;#1077;#1077; #1080; #1086;#1090;#1082;#1088;#1099;#1090;#1086;#1077; #1076;#1074;#1086;#1081;#1085;#1086;#1077; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086;.

#1056;#1072;#1079;#1083;#1080;#1095;#1072;#1102;#1090; #1088;#1072;#1085;#1085;#1077;#1077;, #1087;#1086;#1079;#1076;#1085;#1077;#1077; #1080; #1086;#1090;#1082;#1088;#1099;#1090;#1086;#1077; #1076;#1074;#1086;#1081;#1085;#1086;#1077; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086;. #1059;#1089;#1083;#1086;#1074;#1080;#1103; #1089;#1086;#1076;#1077;#1088;#1078;#1072;#1085;#1080;#1103; #1074; #1087;#1086;#1088;#1103;#1076;#1082;#1077;, #1090;#1072;#1082; #1095;#1090;#1086;. sim; #1086; #8842; sim; #1083; #8842; sim; #1077; {\ displaystyle \ sim _ {o} \ subsetneq \ sim _ {l} \ subsetneq \ sim _ {e}}

#1048;#1079;#1074;#1077;#1089;#1090;#1085;#1086;, #1095;#1090;#1086; #1074; #1085;#1077;#1082;#1086;#1090;#1086;#1088;#1099;#1093; #1089;#1091;#1073;#1074;#1099;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103;#1093;, #1090;#1072;#1082;#1080;#1093; #1082;#1072;#1082; #1072;#1089;#1080;#1085;#1093;#1088;#1086;#1085;#1085;#1086;#1077; #1087;#1080;-#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077;, #1087;#1086;#1079;#1076;#1085;#1077;#1077;, #1088;#1072;#1085;#1085;#1077;#1077; #1080; #1086;#1090;#1082;#1088;#1099;#1090;#1086;#1077; #1076;#1074;#1086;#1081;#1085;#1086;#1077; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086; #1089;#1086;#1074;#1087;#1072;#1076;#1072;#1102;#1090;. #1054;#1076;#1085;#1072;#1082;#1086; #1074; #1101;#1090;#1086;#1084; #1089;#1083;#1091;#1095;#1072;#1077; #1073;#1086;#1083;#1077;#1077; #1087;#1086;#1076;#1093;#1086;#1076;#1103;#1097;#1080;#1084; #1087;#1086;#1085;#1103;#1090;#1080;#1077;#1084; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1072;#1089;#1080;#1085;#1093;#1088;#1086;#1085;#1085;#1086;#1077; #1076;#1074;#1086;#1081;#1085;#1086;#1077; #1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086;. #1042; #1083;#1080;#1090;#1077;#1088;#1072;#1090;#1091;#1088;#1077; #1090;#1077;#1088;#1084;#1080;#1085; #1086;#1090;#1082;#1088;#1099;#1090;#1072;#1103; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1103; #1086;#1073;#1099;#1095;#1085;#1086; #1086;#1090;#1085;#1086;#1089;#1080;#1090;#1089;#1103; #1082; #1073;#1086;#1083;#1077;#1077; #1089;#1083;#1086;#1078;#1085;#1086;#1084;#1091; #1087;#1086;#1085;#1103;#1090;#1080;#1102;, #1074; #1082;#1086;#1090;#1086;#1088;#1086;#1084; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1099; #1080; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1103; #1080;#1085;#1076;#1077;#1082;#1089;#1080;#1088;#1091;#1102;#1090;#1089;#1103; #1089; #1087;#1086;#1084;#1086;#1097;#1100;#1102; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1081; #1088;#1072;#1079;#1083;#1080;#1095;#1080;#1103;; #1087;#1086;#1076;#1088;#1086;#1073;#1085;#1086;#1089;#1090;#1080; #1084;#1086;#1078;#1085;#1086; #1085;#1072;#1081;#1090;#1080; #1074; #1094;#1080;#1090;#1080;#1088;#1086;#1074;#1072;#1085;#1085;#1086;#1081; #1074;#1099;#1096;#1077; #1089;#1090;#1072;#1090;#1100;#1077; #1057;#1072;#1085;#1076;#1078;#1086;#1088;#1076;#1078;#1080;.

#1050;#1086;#1083;#1102;#1095;#1072;#1103; #1101;#1082;#1074;#1080;#1074;#1072;#1083;#1077;#1085;#1090;#1085;#1086;#1089;#1090;#1100;

#1042; #1082;#1072;#1095;#1077;#1089;#1090;#1074;#1077; #1072;#1083;#1100;#1090;#1077;#1088;#1085;#1072;#1090;#1080;#1074;#1099; #1084;#1086;#1078;#1085;#1086; #1086;#1087;#1088;#1077;#1076;#1077;#1083;#1080;#1090;#1100; #1101;#1082;#1074;#1080;#1074;#1072;#1083;#1077;#1085;#1090;#1085;#1086;#1089;#1090;#1100; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1080; #1085;#1077;#1087;#1086;#1089;#1088;#1077;#1076;#1089;#1090;#1074;#1077;#1085;#1085;#1086; #1080;#1079; #1089;#1077;#1084;#1072;#1085;#1090;#1080;#1082;#1080; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080;. #1055;#1080;#1096;#1077;#1084;, #1077;#1089;#1083;#1080; #1087;#1088;#1086;#1094;#1077;#1089;#1089; #1089;#1088;#1072;#1079;#1091; #1088;#1072;#1079;#1088;#1077;#1096;#1072;#1077;#1090; #1074;#1093;#1086;#1076; #1080;#1083;#1080; #1074;#1099;#1093;#1086;#1076; #1087;#1086; #1080;#1084;#1077;#1085;#1080;. #1087; dArr; #1072; {\ displaystyle p \ Downarrow a} #1087; {\ displaystyle p} #1072; {\ displaystyle a}

#1041;#1080;#1085;#1072;#1088;#1085;#1086;#1077; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1077; #1085;#1072;#1076; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072;#1084;#1080; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1073;#1080;#1079;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1077;#1081; #1089; #1079;#1072;#1079;#1091;#1073;#1088;#1080;#1085;#1072;#1084;#1080;, #1077;#1089;#1083;#1080; #1101;#1090;#1086; #1089;#1080;#1084;#1084;#1077;#1090;#1088;#1080;#1095;#1085;#1086;#1077; #1086;#1090;#1085;#1086;#1096;#1077;#1085;#1080;#1077;, #1091;#1076;#1086;#1074;#1083;#1077;#1090;#1074;#1086;#1088;#1103;#1102;#1097;#1077;#1077; #1090;#1086;#1084;#1091;, #1095;#1090;#1086; #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1081; #1087;#1072;#1088;#1099; #1101;#1083;#1077;#1084;#1077;#1085;#1090;#1086;#1074; #1084;#1099; #1080;#1084;#1077;#1077;#1084; #1088; {\ displaystyle R} ( #1087; , q ) isin; #1088; {\ displaystyle (p, q) \ in R}

(1) #1090;#1086;#1075;#1076;#1072; #1080; #1090;#1086;#1083;#1100;#1082;#1086; #1090;#1086;#1075;#1076;#1072;, #1082;#1086;#1075;#1076;#1072; #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1075;#1086; #1080;#1084;#1077;#1085;#1080; #1087; dArr; #1072; {\ displaystyle p \ Downarrow a} q dArr; #1072; {\ displaystyle q \ Downarrow a} #1072; {\ displaystyle a}

#1072; #1090;#1072;#1082;#1078;#1077;

(2) #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1081; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1080; #1089;#1091;#1097;#1077;#1089;#1090;#1074;#1091;#1077;#1090; #1088;#1077;#1076;#1091;#1082;#1094;#1080;#1103; #1087; rarr; #1087; prime; {\ displaystyle p \ rightarrow p '} q rarr; q prime; {\ displaystyle q \ rightarrow q '}

#1090;#1072;#1082;#1086;#1081; #1095;#1090;#1086;. ( #1087; prime; , q prime; ) isin; #1088; {\ displaystyle (p ', q') \ in R}

#1052;#1099; #1075;#1086;#1074;#1086;#1088;#1080;#1084;, #1095;#1090;#1086; #1080; #1103;#1074;#1083;#1103;#1102;#1090;#1089;#1103; #1082;#1086;#1083;#1102;#1095;#1077;#1081; bisimilar, #1077;#1089;#1083;#1080; #1089;#1091;#1097;#1077;#1089;#1090;#1074;#1091;#1077;#1090; #1082;#1086;#1083;#1102;#1095;#1072;#1103; #1073;#1080;#1089;#1080;#1084;#1091;#1083;#1103;#1094;#1080;#1102; #1075;#1076;#1077;. #1087; {\ displaystyle p} q {\ displaystyle q} #1088; {\ displaystyle R} ( #1087; , q ) isin; #1088; {\ displaystyle (p, q) \ in R}

#1054;#1087;#1088;#1077;#1076;#1077;#1083;#1103;#1103; #1082;#1086;#1085;#1090;#1077;#1082;#1089;#1090; #1082;#1072;#1082; pi;- #1095;#1083;#1077;#1085; #1089; #1086;#1090;#1074;#1077;#1088;#1089;#1090;#1080;#1077;#1084; [], #1084;#1099; #1075;#1086;#1074;#1086;#1088;#1080;#1084;, #1095;#1090;#1086; #1076;#1074;#1072; #1087;#1088;#1086;#1094;#1077;#1089;#1089;#1072; P #1080; Q #1103;#1074;#1083;#1103;#1102;#1090;#1089;#1103; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1099;#1084;#1080; #1089; #1079;#1072;#1079;#1091;#1073;#1088;#1080;#1085;#1072;#1084;#1080;, #1079;#1072;#1087;#1080;#1089;#1072;#1085;#1085;#1099;#1084;#1080;, #1077;#1089;#1083;#1080; #1076;#1083;#1103; #1082;#1072;#1078;#1076;#1086;#1075;#1086; #1082;#1086;#1085;#1090;#1077;#1082;#1089;#1090;#1072; #1086;#1085;#1080; #1077;#1089;#1090;#1100;, #1080; #1079;#1072;#1086;#1089;#1090;#1088;#1077;#1085;#1099; #1076;#1074;#1086;#1103;#1082;#1080;#1084;#1080;. #1054;#1082;#1072;#1079;#1099;#1074;#1072;#1077;#1090;#1089;#1103;, #1082;#1086;#1083;#1102;#1095;#1072;#1103; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1090;#1085;#1086;#1089;#1090;#1100; #1089;#1086;#1074;#1087;#1072;#1076;#1072;#1077;#1090; #1089; #1082;#1086;#1085;#1075;#1088;#1091;#1101;#1085;#1094;#1080;#1077;#1081;, #1080;#1085;#1076;#1091;#1094;#1080;#1088;#1086;#1074;#1072;#1085;#1085;#1086;#1081; #1088;#1072;#1085;#1085;#1080;#1084; #1073;#1080;#1089;#1093;#1086;#1076;#1089;#1090;#1074;#1086;#1084;. #1087; sim; #1073; Q {\ Displaystyle P \ sim _ {b} Q \, \!} C [ ] {\ displaystyle C []} C [ #1087; ] {\ displaystyle C [P]} C [ Q ] {\ displaystyle C [Q]}

#1055;#1088;#1080;#1083;#1086;#1078;#1077;#1085;#1080;#1103;

Pi; -#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077; #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1091;#1077;#1090;#1089;#1103; #1076;#1083;#1103; #1086;#1087;#1080;#1089;#1072;#1085;#1080;#1103; #1088;#1072;#1079;#1083;#1080;#1095;#1085;#1099;#1093; #1074;#1080;#1076;#1086;#1074; #1087;#1072;#1088;#1072;#1083;#1083;#1077;#1083;#1100;#1085;#1099;#1093; #1089;#1080;#1089;#1090;#1077;#1084;. #1060;#1072;#1082;#1090;#1080;#1095;#1077;#1089;#1082;#1080;, #1085;#1077;#1082;#1086;#1090;#1086;#1088;#1099;#1077; #1080;#1079; #1089;#1072;#1084;#1099;#1093; #1087;#1086;#1089;#1083;#1077;#1076;#1085;#1080;#1093; #1087;#1088;#1080;#1083;#1086;#1078;#1077;#1085;#1080;#1081; #1083;#1077;#1078;#1072;#1090; #1079;#1072; #1087;#1088;#1077;#1076;#1077;#1083;#1072;#1084;#1080; #1086;#1073;#1083;#1072;#1089;#1090;#1080; #1090;#1088;#1072;#1076;#1080;#1094;#1080;#1086;#1085;#1085;#1086;#1081; #1080;#1085;#1092;#1086;#1088;#1084;#1072;#1090;#1080;#1082;#1080;.

#1042; 1997 #1075;#1086;#1076;#1091; #1052;#1072;#1088;#1090;#1080;#1085; #1040;#1073;#1072;#1076;#1080; #1080; #1069;#1085;#1076;#1088;#1102; #1043;#1086;#1088;#1076;#1086;#1085; #1087;#1088;#1077;#1076;#1083;#1086;#1078;#1080;#1083;#1080; #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1077; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103;, Spi-#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077;, #1082;#1072;#1082; #1092;#1086;#1088;#1084;#1072;#1083;#1100;#1085;#1091;#1102; #1085;#1086;#1090;#1072;#1094;#1080;#1102; #1076;#1083;#1103; #1086;#1087;#1080;#1089;#1072;#1085;#1080;#1103; #1080; #1088;#1072;#1089;#1089;#1091;#1078;#1076;#1077;#1085;#1080;#1081; #1086; #1082;#1088;#1080;#1087;#1090;#1086;#1075;#1088;#1072;#1092;#1080;#1095;#1077;#1089;#1082;#1080;#1093; #1087;#1088;#1086;#1090;#1086;#1082;#1086;#1083;#1072;#1093;. Spi-#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077; #1088;#1072;#1089;#1096;#1080;#1088;#1103;#1077;#1090; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077; #1087;#1088;#1080;#1084;#1080;#1090;#1080;#1074;#1072;#1084;#1080; #1076;#1083;#1103; #1096;#1080;#1092;#1088;#1086;#1074;#1072;#1085;#1080;#1103; #1080; #1076;#1077;#1096;#1080;#1092;#1088;#1086;#1074;#1072;#1085;#1080;#1103;. #1042; 2001 #1075;#1086;#1076;#1091; #1052;#1072;#1088;#1090;#1080;#1085; #1040;#1073;#1072;#1076;#1080; #1080; #1057;#1077;#1076;#1088;#1080;#1082; #1060;#1091;#1088;#1085;#1077;#1090; #1086;#1073;#1086;#1073;#1097;#1080;#1083;#1080; #1086;#1073;#1088;#1072;#1073;#1086;#1090;#1082;#1091; #1082;#1088;#1080;#1087;#1090;#1086;#1075;#1088;#1072;#1092;#1080;#1095;#1077;#1089;#1082;#1080;#1093; #1087;#1088;#1086;#1090;#1086;#1082;#1086;#1083;#1086;#1074; #1076;#1083;#1103; #1089;#1086;#1079;#1076;#1072;#1085;#1080;#1103; #1087;#1088;#1080;#1082;#1083;#1072;#1076;#1085;#1086;#1075;#1086; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103;. #1042; #1085;#1072;#1089;#1090;#1086;#1103;#1097;#1077;#1077; #1074;#1088;#1077;#1084;#1103; #1089;#1091;#1097;#1077;#1089;#1090;#1074;#1091;#1077;#1090; #1073;#1086;#1083;#1100;#1096;#1086;#1081; #1086;#1073;#1098;#1077;#1084; #1088;#1072;#1073;#1086;#1090;, #1087;#1086;#1089;#1074;#1103;#1097;#1077;#1085;#1085;#1099;#1093; #1074;#1072;#1088;#1080;#1072;#1085;#1090;#1072;#1084; #1087;#1088;#1080;#1082;#1083;#1072;#1076;#1085;#1086;#1075;#1086; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103;, #1074;#1082;#1083;#1102;#1095;#1072;#1103; #1088;#1103;#1076; #1080;#1085;#1089;#1090;#1088;#1091;#1084;#1077;#1085;#1090;#1086;#1074; #1101;#1082;#1089;#1087;#1077;#1088;#1080;#1084;#1077;#1085;#1090;#1072;#1083;#1100;#1085;#1086;#1081; #1087;#1088;#1086;#1074;#1077;#1088;#1082;#1080;. #1054;#1076;#1085;#1080;#1084; #1080;#1079; #1087;#1088;#1080;#1084;#1077;#1088;#1086;#1074; #1103;#1074;#1083;#1103;#1077;#1090;#1089;#1103; #1080;#1085;#1089;#1090;#1088;#1091;#1084;#1077;#1085;#1090; ProVerif [2], #1089;#1086;#1079;#1076;#1072;#1085;#1085;#1099;#1081; #1041;#1088;#1091;#1085;#1086; #1041;#1083;#1072;#1085;#1096;#1077;, #1086;#1089;#1085;#1086;#1074;#1072;#1085;#1085;#1099;#1081; #1085;#1072; #1087;#1077;#1088;#1077;#1074;#1086;#1076;#1077; #1087;#1088;#1080;#1084;#1077;#1085;#1103;#1077;#1084;#1086;#1075;#1086; pi; -#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103; #1074; #1089;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1091; #1083;#1086;#1075;#1080;#1095;#1077;#1089;#1082;#1086;#1075;#1086; #1087;#1088;#1086;#1075;#1088;#1072;#1084;#1084;#1080;#1088;#1086;#1074;#1072;#1085;#1080;#1103; #1041;#1083;#1072;#1085;#1096;#1077;. #1044;#1088;#1091;#1075;#1086;#1081; #1087;#1088;#1080;#1084;#1077;#1088; - Cryptyc [3], #1089;#1086;#1079;#1076;#1072;#1085;#1085;#1099;#1081; #1069;#1085;#1076;#1088;#1102; #1043;#1086;#1088;#1076;#1086;#1085;#1086;#1084; #1080; #1040;#1083;#1072;#1085;#1086;#1084; #1044;#1078;#1077;#1092;#1092;#1088;#1080;, #1082;#1086;#1090;#1086;#1088;#1099;#1081; #1080;#1089;#1087;#1086;#1083;#1100;#1079;#1091;#1077;#1090; #1084;#1077;#1090;#1086;#1076; #1091;#1090;#1074;#1077;#1088;#1078;#1076;#1077;#1085;#1080;#1081; #1089;#1086;#1086;#1090;#1074;#1077;#1090;#1089;#1090;#1074;#1080;#1103; #1042;#1091; #1080; #1051;#1101;#1084;#1072; #1074; #1082;#1072;#1095;#1077;#1089;#1090;#1074;#1077; #1086;#1089;#1085;#1086;#1074;#1099; #1076;#1083;#1103; #1089;#1080;#1089;#1090;#1077;#1084; #1090;#1080;#1087;#1086;#1074;, #1082;#1086;#1090;#1086;#1088;#1099;#1077; #1084;#1086;#1075;#1091;#1090; #1087;#1088;#1086;#1074;#1077;#1088;#1103;#1090;#1100; #1089;#1074;#1086;#1081;#1089;#1090;#1074;#1072; #1072;#1091;#1090;#1077;#1085;#1090;#1080;#1092;#1080;#1082;#1072;#1094;#1080;#1080; #1082;#1088;#1080;#1087;#1090;#1086;#1075;#1088;#1072;#1092;#1080;#1095;#1077;#1089;#1082;#1080;#1093; #1087;#1088;#1086;#1090;#1086;#1082;#1086;#1083;#1086;#1074;.

#1055;#1088;#1080;#1084;#1077;#1088;#1085;#1086; #1074; 2002 #1075;#1086;#1076;#1091; #1061;#1086;#1074;#1072;#1088;#1076; #1057;#1084;#1080;#1090; #1080; #1055;#1080;#1090;#1077;#1088; #1060;#1080;#1085;#1075;#1072;#1088; #1079;#1072;#1080;#1085;#1090;#1077;#1088;#1077;#1089;#1086;#1074;#1072;#1083;#1080;#1089;#1100; #1090;#1077;#1084;, #1095;#1090;#1086; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077; #1089;#1090;#1072;#1085;#1077;#1090; #1080;#1085;#1089;#1090;#1088;#1091;#1084;#1077;#1085;#1090;#1086;#1084; #1086;#1087;#1080;#1089;#1072;#1085;#1080;#1103; #1076;#1083;#1103; #1084;#1086;#1076;#1077;#1083;#1080;#1088;#1086;#1074;#1072;#1085;#1080;#1103; #1073;#1080;#1079;#1085;#1077;#1089;-#1087;#1088;#1086;#1094;#1077;#1089;#1089;#1086;#1074;. #1050; #1080;#1102;#1083;#1102; 2006 #1075;#1086;#1076;#1072; #1074; #1089;#1086;#1086;#1073;#1097;#1077;#1089;#1090;#1074;#1077; #1086;#1073;#1089;#1091;#1078;#1076;#1072;#1077;#1090;#1089;#1103;, #1085;#1072;#1089;#1082;#1086;#1083;#1100;#1082;#1086; #1101;#1090;#1086; #1073;#1099;#1083;#1086; #1073;#1099; #1087;#1086;#1083;#1077;#1079;#1085;#1086;. #1057;#1086;#1074;#1089;#1077;#1084; #1085;#1077;#1076;#1072;#1074;#1085;#1086; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077; #1089;#1092;#1086;#1088;#1084;#1080;#1088;#1086;#1074;#1072;#1083;#1086; #1090;#1077;#1086;#1088;#1077;#1090;#1080;#1095;#1077;#1089;#1082;#1091;#1102; #1086;#1089;#1085;#1086;#1074;#1091; #1103;#1079;#1099;#1082;#1072; #1084;#1086;#1076;#1077;#1083;#1080;#1088;#1086;#1074;#1072;#1085;#1080;#1103; #1073;#1080;#1079;#1085;#1077;#1089;-#1087;#1088;#1086;#1094;#1077;#1089;#1089;#1086;#1074; (BPML) #1080; Microsoft XLANG.

Pi; -#1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1077; #1090;#1072;#1082;#1078;#1077; #1087;#1088;#1080;#1074;#1083;#1077;#1082;#1072;#1077;#1090; #1080;#1085;#1090;#1077;#1088;#1077;#1089; #1082; #1084;#1086;#1083;#1077;#1082;#1091;#1083;#1103;#1088;#1085;#1086;#1081; #1073;#1080;#1086;#1083;#1086;#1075;#1080;#1080;. #1042; 1999 #1075;#1086;#1076;#1091; #1040;#1074;#1080;#1074; #1056;#1077;#1075;#1077;#1074; #1080; #1069;#1093;#1091;#1076; #1064;#1072;#1087;#1080;#1088;#1086; #1087;#1086;#1082;#1072;#1079;#1072;#1083;#1080;, #1095;#1090;#1086; #1084;#1086;#1078;#1085;#1086; #1086;#1087;#1080;#1089;#1072;#1090;#1100; #1082;#1083;#1077;#1090;#1086;#1095;#1085;#1099;#1081; #1089;#1080;#1075;#1085;#1072;#1083;#1100;#1085;#1099;#1081; #1087;#1091;#1090;#1100; (#1090;#1072;#1082; #1085;#1072;#1079;#1099;#1074;#1072;#1077;#1084;#1099;#1081; #1082;#1072;#1089;#1082;#1072;#1076; RTK / MAPK ) #1080;, #1074; #1095;#1072;#1089;#1090;#1085;#1086;#1089;#1090;#1080;, #1084;#1086;#1083;#1077;#1082;#1091;#1083;#1103;#1088;#1085;#1099;#1081; laquo;#1083;#1077;#1075;#1086;raquo;, #1082;#1086;#1090;#1086;#1088;#1099;#1081; #1088;#1077;#1072;#1083;#1080;#1079;#1091;#1077;#1090; #1101;#1090;#1080; #1079;#1072;#1076;#1072;#1095;#1080; #1082;#1086;#1084;#1084;#1091;#1085;#1080;#1082;#1072;#1094;#1080;#1080; #1074; #1088;#1072;#1089;#1096;#1080;#1088;#1077;#1085;#1080;#1080; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103;. #1055;#1086;#1089;#1083;#1077; #1101;#1090;#1086;#1081; #1086;#1089;#1085;#1086;#1074;#1086;#1087;#1086;#1083;#1072;#1075;#1072;#1102;#1097;#1077;#1081; #1089;#1090;#1072;#1090;#1100;#1080; #1076;#1088;#1091;#1075;#1080;#1077; #1072;#1074;#1090;#1086;#1088;#1099; #1086;#1087;#1080;#1089;#1072;#1083;#1080; #1074;#1089;#1102; #1084;#1077;#1090;#1072;#1073;#1086;#1083;#1080;#1095;#1077;#1089;#1082;#1091;#1102; #1089;#1077;#1090;#1100; #1084;#1080;#1085;#1080;#1084;#1072;#1083;#1100;#1085;#1086;#1081; #1082;#1083;#1077;#1090;#1082;#1080;. #1042; 2009 #1075;#1086;#1076;#1091; #1069;#1085;#1090;#1086;#1085;#1080; #1053;#1101;#1096; #1080; #1057;#1072;#1088;#1072; #1050;#1072;#1083;#1074;#1072;#1083;#1072; #1087;#1088;#1077;#1076;#1083;#1086;#1078;#1080;#1083;#1080; #1089;#1090;#1088;#1091;#1082;#1090;#1091;#1088;#1091; pi;- #1080;#1089;#1095;#1080;#1089;#1083;#1077;#1085;#1080;#1103; #1076;#1083;#1103; #1084;#1086;#1076;#1077;#1083;#1080;#1088;#1086;#1074;#1072;#1085;#1080;#1103; #1087;#1077;#1088;#1077;#1076;#1072;#1095;#1080; #1089;#1080;#1075;#1085;#1072;#1083;#1072;, #1082;#1086;#1090;#1086;#1088;#1099;#1081; #1091;#1087;#1088;#1072;#1074;#1083;#1103;#1077;#1090; #1072;#1075;#1088;#1077;#1075;#1072;#1094;#1080;#1077;#1081; Dictyostelium discoideum.

#1048;#1089;#1090;#1086;#1088;#1080;#1103;

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Последняя правка сделана 2023-03-19 06:45:15
Содержание доступно по лицензии CC BY-SA 3.0 (если не указано иное).
Обратная связь: support@alphapedia.ru
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О проекте