Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà)

   Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà).   Êàæäîå
   ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿå...
Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà)

   Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà).   Êàæäîå
   ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿå...
Ïåðå÷èñëèìûå ìíîæåñòâà
Ïåðå÷èñëèìûå ìíîæåñòâà

  Îïðåäåëåíèå.                                          n
                 Ìíîæåñòâî M, ñîñòîÿùåå ...
Ïåðå÷èñëèìûå ìíîæåñòâà

  Îïðåäåëåíèå.                                          n
                 Ìíîæåñòâî M, ñîñòîÿùåå ...
Ïåðå÷èñëèìûå ìíîæåñòâà
Ïåðå÷èñëèìûå ìíîæåñòâà

  Îïðåäåëåíèå.   Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ
  ïåðå÷èñëèìûì, åñëè ìîæíî íàïèñàòü ïðîã...
Ðåãèñòðîâûå ìàøèíû
Ðåãèñòðîâûå ìàøèíû

  Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî  ðåãèñòðîâ
          n
  R1, . . . ,R êàæäûé èç êîòîðûõ...
Ðåãèñòðîâûå ìàøèíû

  Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî      ðåãèñòðîâ
            n
  R1, . . . ,R êàæäûé èç ê...
Ðåãèñòðîâûå ìàøèíû

  Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî      ðåãèñòðîâ
            n
  R1, . . . ,R êàæäûé èç ê...
Ðåãèñòðîâûå ìàøèíû

  Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî      ðåãèñòðîâ
            n
  R1, . . . ,R êàæäûé èç ê...
Ðåãèñòðîâûå ìàøèíû

  Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî      ðåãèñòðîâ
              n
  R1, . . . ,R êàæäûé èç...
Ðåãèñòðîâûå ìàøèíû

  Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî      ðåãèñòðîâ
               n
  R1, . . . ,R êàæäûé è...
Ïåðå÷èñëèìûå ìíîæåñòâà
Ïåðå÷èñëèìûå ìíîæåñòâà

  Îïðåäåëåíèå.   Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ
  ïåðå÷èñëèìûì, åñëè ìîæíî íàïèñàòü ïðîã...
Ïåðå÷èñëèìûå ìíîæåñòâà

  Îïðåäåëåíèå.   Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ
  ïåðå÷èñëèìûì, åñëè ìîæíî íàïèñàòü ïðîã...
Ïðèìåð

   S1:   R1−−;   S2;   S8
   S2:   R1−−;   S3;   S9
   S3:   R2++;   S4
   S4:   R1−−;   S5;   S6
   S5:   R1−−;  ...
Óðàâíåíèÿ ñ ïàðàìåòðàìè

  Ñåìåéñòâî äèîôàíòîâûõ óðàâíåíèé èìååò âèä
                  M (a1, . . . , an , x1, . . . , xm ...
Óðàâíåíèÿ ñ ïàðàìåòðàìè

  Ñåìåéñòâî äèîôàíòîâûõ óðàâíåíèé èìååò âèä
                  M (a1, . . . , an , x1, . . . , xm ...
Óðàâíåíèÿ ñ ïàðàìåòðàìè

  Ñåìåéñòâî äèîôàíòîâûõ óðàâíåíèé èìååò âèä
                  M (a1, . . . , an , x1, . . . , xm ...
Óðàâíåíèÿ ñ ïàðàìåòðàìè

  Ñåìåéñòâî äèîôàíòîâûõ óðàâíåíèé èìååò âèä
                  M (a1, . . . , an , x1, . . . , xm ...
Äèîôàíòîâû ìàøèíû

  Leonard Adleman è Kenneth Manders [1976] ââåëè ïîíÿòèå
  íåäåòåðìèíèðîâàííîé äèîôàíòîâîé ìàøèíû    , ...
Äèîôàíòîâû ìàøèíû

  Leonard Adleman è Kenneth Manders [1976] ââåëè ïîíÿòèå
  íåäåòåðìèíèðîâàííîé äèîôàíòîâîé ìàøèíû    , ...
Äèîôàíòîâû ìàøèíû

  Leonard Adleman è Kenneth Manders [1976] ââåëè ïîíÿòèå
  íåäåòåðìèíèðîâàííîé äèîôàíòîâîé ìàøèíû    , ...
Äèîôàíòîâà ñëîæíîñòü




                             NDDM
          âõîä -                                  óãàäàòü
     ...
Äèîôàíòîâà ñëîæíîñòü




                                  NDDM
              âõîä -                                   óãà...
Äèîôàíòîâà ñëîæíîñòü

  Leonard Adleman è Kenneth Manders [1975] ââåëè â
  ðàññìîòðåíèå êëàññ D ñîñòîÿùèé èç ìíîæåñòâ M èì...
Äèîôàíòîâà ñëîæíîñòü

  Leonard Adleman è Kenneth Manders [1975] ââåëè â
  ðàññìîòðåíèå êëàññ D ñîñòîÿùèé èç ìíîæåñòâ M èì...
Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà)

   Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà).   Êàæäîå
   ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿå...
Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà)

   Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà).   Êàæäîå
   ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿå...
Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà)

   Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà).   Êàæäîå
   ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿå...
Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà)

   Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà).   Êàæäîå
   ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿå...
Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà)

   Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà).   Êàæäîå
   ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿå...
Ïðîòîêîë


                       q      ...   t +1 t          ...    0
               S1     s1,q    ...   s1,t+1 s1,t   ...
Ïðîòîêîë


                  q     ...   t +1 t          ...    0
            .
            .     .
                  .   ...
Ïðîòîêîë

                 q     ...   t +1       t     ...    0
           .
           .     .
                 .      ....
Ïðèìåð

   S1:R1−−; S2; S8   S4:R1−−; S5; S6   S7:R1++; S6
   S2:R1−−; S3; S9   S5:R1−−; S3; S8   S8:R1++; S8
   S3:R2++; ...
Ïðèìåð

   S1:R1−−; S2; S8   S4:R1−−; S5; S6   S7:R1++; S6
   S2:R1−−; S3; S9   S5:R1−−; S3; S8   S8:R1++; S8
   S3:R2++; ...
Ïðèìåð

   S1:R1−−; S2; S8   S4:R1−−; S5; S6   S7:R1++; S6
   S2:R1−−; S3; S9   S5:R1−−; S3; S8   S8:R1++; S8
   S3:R2++; ...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6   S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8   S8:R1++; S8
  ...
Ïðèìåð

   S1:R1−−; S2; S8      S4:R1−−; S5; S6   S7:R1++; S6
   S2:R1−−; S3; S9      S5:R1−−; S3; S8   S8:R1++; S8
   S3:...
Ïðèìåð

   S1:R1−−; S2; S8       S4:R1−−; S5; S6     S7:R1++; S6
   S2:R1−−; S3; S9       S5:R1−−; S3; S8     S8:R1++; S8
...
Ïðèìåð

   S1:R1−−; S2; S8       S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9       S5:R1−−; S3; S8         S8:R...
Ïðèìåð

   S1:R1−−; S2; S8       S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9       S5:R1−−; S3; S8         S8:R...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Ïðèìåð

   S1:R1−−; S2; S8        S4:R1−−; S5; S6         S7:R1++; S6
   S2:R1−−; S3; S9        S5:R1−−; S3; S8         S8...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ



                      r ,t + 1 = r ,t +   +
                                              sk ,...
Íîâûå ñîñòîÿíèÿ



                  sd ,t+1 =   d sk ,t +
                              +
                               ...
Ïðîòîêîë


           q   ...   t +1 t           ...    0
    .
    .      .
           .    .
                .       .
 ...
Ïðîòîêîë


           q   ...   t +1 t           ...    0
    .
    .      .
           .    .
                .       .
 ...
Ïðîòîêîë


           q   ...   t +1 t           ...    0
    .
    .      .
           .    .
                .       .
 ...
Ïðîòîêîë


           q   ...   t +1 t           ...    0
    .
    .      .
           .    .
                .       .
 ...
Ïðîòîêîë


           q   ...   t +1 t           ...    0
    .
    .      .
           .    .
                .       .
 ...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ


                    q                              q                             q
            ...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ


                    q                              q                             q
            ...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ


                    q                              q                             q
            ...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ


                    q                              q                             q
            ...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ


                     q                           q                           q
            sk =...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ


                            q                          q                           q
          ...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ


                            q                          q                           q
          ...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ


                            q                          q                           q
          ...
Íîâûå çíà÷åíèÿ ðåãèñòðîâ


                             q                           q                           q
        ...
Íîâûå ñîñòîÿíèÿ


                                q                             q
                        sk =          sk...
Íîâûå ñîñòîÿíèÿ


                                q                             q
                        sk =          sk...
Íîâûå ñîñòîÿíèÿ


                                q                             q
                        sk =          sk...
Íîâûå ñîñòîÿíèÿ


                                q                             q
                        sk =          sk...
Íîâûå ñîñòîÿíèÿ


                                  q                           q
                         sk =          s...
Íîâûå ñîñòîÿíèÿ


                                     q                           q
                            sk =     ...
Íîâûå ñîñòîÿíèÿ


                                     q                           q
                            sk =     ...
Íîâûå ñîñòîÿíèÿ


                                     q                           q
                            sk =     ...
Íîâûå ñîñòîÿíèÿ


                                     q                           q
                            sk =     ...
Èíäèêàòîðû íóëÿ




             z ,t =          r
                      0, åñëè ,t = 0
                      1 â ïðîòèâíî...
Èíäèêàòîðû íóëÿ




             z ,t =             r
                         0, åñëè ,t = 0
                         1 â...
Èíäèêàòîðû íóëÿ




             z ,t =             r
                         0, åñëè ,t = 0
                         1 â...
Èíäèêàòîðû íóëÿ




               z ,t =              r
                            0, åñëè ,t = 0
                      ...
Èíäèêàòîðû íóëÿ




               z ,t =               r
                            0, åñëè ,t = 0
                     ...
Èíäèêàòîðû íóëÿ




               z ,t =               r
                            0, åñëè ,t = 0
                     ...
Èíäèêàòîðû íóëÿ




                   z ,t =             r
                              0, åñëè ,t = 0
                 ...
Èíäèêàòîðû íóëÿ




                     z ,t =             r
                                0, åñëè ,t = 0
             ...
Âûáîð   c

            r ,t  b
Âûáîð   c

            r , t  b = 2 c +1
Âûáîð   c

               r , t  b = 2 c +1    r ,t ≤ 2c − 1 = 01 . . . 1
            2c − 1 +   r ,t =                  r...
Âûáîð   c

               r , t  b = 2 c +1    r ,t ≤ 2c − 1 = 01 . . . 1
            2c − 1 +   r ,t =                  r...
Âûáîð   c

               r , t  b = 2 c +1      r ,t ≤ 2c − 1 = 01 . . . 1
            2c − 1 +   r ,t =                 ...
Âûáîð   c

               r , t  b = 2 c +1      r ,t ≤ 2c − 1 = 01 . . . 1
            2c − 1 +   r ,t =                 ...
Âûáîð   c

               r , t  b = 2 c +1      r ,t ≤ 2c − 1 = 01 . . . 1
            2c − 1 +   r ,t =                 ...
Âûáîð   c

               r , t  b = 2 c +1           r ,t ≤ 2c − 1 = 01 . . . 1
            2c − 1 +   r ,t =            ...
Âûáîð   c

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Юрий Владимирович Матиясевич. Десятая проблема Гильберта. Решение и применения в информатике. Лекция 03

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Юрий Владимирович Матиясевич. Десятая проблема Гильберта. Решение и применения в информатике. Лекция 03

  1. 1. Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà) Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà). Êàæäîå ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿåòñÿ äèîôàíòîâûì.
  2. 2. Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà) Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà). Êàæäîå ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿåòñÿ äèîôàíòîâûì.
  3. 3. Ïåðå÷èñëèìûå ìíîæåñòâà
  4. 4. Ïåðå÷èñëèìûå ìíîæåñòâà Îïðåäåëåíèå. n Ìíîæåñòâî M, ñîñòîÿùåå èç -îê íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì , åñëè ìîæíî íàïèñàòü ïðîãðàììó R, òàêóþ ÷òî a1 , . . . , an -  îñòàíîâêà, åñëè a1 , . . . , an ∈ M R - âå÷íàÿ ðàáîòà â ïðîòèâíîì ñëó÷àå
  5. 5. Ïåðå÷èñëèìûå ìíîæåñòâà Îïðåäåëåíèå. n Ìíîæåñòâî M, ñîñòîÿùåå èç -îê íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì , åñëè ìîæíî íàïèñàòü ïðîãðàììó R, òàêóþ ÷òî a1 , . . . , an -  îñòàíîâêà, åñëè a1 , . . . , an ∈ M R - âå÷íàÿ ðàáîòà â ïðîòèâíîì ñëó÷àå Ýêâèâàëåíòíîå îïðåäåëåíèå. Ìíîæåñòâî M, ñîñòîÿùåå èç n-îê íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì, åñëè ìîæíî íàïèñàòü ïðîãðàììó P êîòîðàÿ (ðàáîòàÿ áåñêîíå÷íî äîëãî) áóäåò ïå÷àòàòü òîëüêî ýëåìåíòû ìíîæåñòâà M è íàïå÷àòàåò êàæäîå èç íèõ, áûòü ìîæåò, ìíîãî ðàç.
  6. 6. Ïåðå÷èñëèìûå ìíîæåñòâà
  7. 7. Ïåðå÷èñëèìûå ìíîæåñòâà Îïðåäåëåíèå. Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì, åñëè ìîæíî íàïèñàòü ïðîãðàììó R, òàêóþ ÷òî a  îñòàíîâêà, åñëè a∈M R - - âå÷íàÿ ðàáîòà â ïðîòèâíîì ñëó÷àå
  8. 8. Ðåãèñòðîâûå ìàøèíû
  9. 9. Ðåãèñòðîâûå ìàøèíû Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî ðåãèñòðîâ n R1, . . . ,R êàæäûé èç êîòîðûõ ìîæåò ñîäåðæàòü ïðîèçâîëüíî áîëüøîå íàòóðàëüíîå ÷èñëî.
  10. 10. Ðåãèñòðîâûå ìàøèíû Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî ðåãèñòðîâ n R1, . . . ,R êàæäûé èç êîòîðûõ ìîæåò ñîäåðæàòü ïðîèçâîëüíî áîëüøîå íàòóðàëüíîå ÷èñëî. Ìàøèíà âûïîëíÿåò ïðîãðàììó ñîñòîÿùóþ èç êîíå÷íîãî ÷èñëà èíñòðóêöèé ñíàáæåííûõ ìåòêàìè m S1, . . . ,S . Êîãäà ìàøèíà âûïîëíÿåò èíñòðóêöèþ ñ k ìåòêîé S , ìû ãîâîðèì, ÷òî ìàøèíà íàõîäèòñÿ â ñîñòîÿíèè k S .
  11. 11. Ðåãèñòðîâûå ìàøèíû Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî ðåãèñòðîâ n R1, . . . ,R êàæäûé èç êîòîðûõ ìîæåò ñîäåðæàòü ïðîèçâîëüíî áîëüøîå íàòóðàëüíîå ÷èñëî. Ìàøèíà âûïîëíÿåò ïðîãðàììó ñîñòîÿùóþ èç êîíå÷íîãî ÷èñëà èíñòðóêöèé ñíàáæåííûõ ìåòêàìè m S1, . . . ,S . Êîãäà ìàøèíà âûïîëíÿåò èíñòðóêöèþ ñ k ìåòêîé S , ìû ãîâîðèì, ÷òî ìàøèíà íàõîäèòñÿ â ñîñòîÿíèè k S . Èíñòðóêöèè áûâàþò òð¼õ òèïîâ:
  12. 12. Ðåãèñòðîâûå ìàøèíû Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî ðåãèñòðîâ n R1, . . . ,R êàæäûé èç êîòîðûõ ìîæåò ñîäåðæàòü ïðîèçâîëüíî áîëüøîå íàòóðàëüíîå ÷èñëî. Ìàøèíà âûïîëíÿåò ïðîãðàììó ñîñòîÿùóþ èç êîíå÷íîãî ÷èñëà èíñòðóêöèé ñíàáæåííûõ ìåòêàìè m S1, . . . ,S . Êîãäà ìàøèíà âûïîëíÿåò èíñòðóêöèþ ñ k ìåòêîé S , ìû ãîâîðèì, ÷òî ìàøèíà íàõîäèòñÿ â ñîñòîÿíèè k S . Èíñòðóêöèè áûâàþò òð¼õ òèïîâ: k I. S : R + +;S i
  13. 13. Ðåãèñòðîâûå ìàøèíû Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî ðåãèñòðîâ n R1, . . . ,R êàæäûé èç êîòîðûõ ìîæåò ñîäåðæàòü ïðîèçâîëüíî áîëüøîå íàòóðàëüíîå ÷èñëî. Ìàøèíà âûïîëíÿåò ïðîãðàììó ñîñòîÿùóþ èç êîíå÷íîãî ÷èñëà èíñòðóêöèé ñíàáæåííûõ ìåòêàìè m S1, . . . ,S . Êîãäà ìàøèíà âûïîëíÿåò èíñòðóêöèþ ñ k ìåòêîé S , ìû ãîâîðèì, ÷òî ìàøèíà íàõîäèòñÿ â ñîñòîÿíèè k S . Èíñòðóêöèè áûâàþò òð¼õ òèïîâ: k I. S : R + +;S i II. Sk : R − −; S ;Si j
  14. 14. Ðåãèñòðîâûå ìàøèíû Ðåãèñòðîâàÿ ìàøèíà èìååò êîíå÷íîå êîëè÷åñòâî ðåãèñòðîâ n R1, . . . ,R êàæäûé èç êîòîðûõ ìîæåò ñîäåðæàòü ïðîèçâîëüíî áîëüøîå íàòóðàëüíîå ÷èñëî. Ìàøèíà âûïîëíÿåò ïðîãðàììó ñîñòîÿùóþ èç êîíå÷íîãî ÷èñëà èíñòðóêöèé ñíàáæåííûõ ìåòêàìè m S1, . . . ,S . Êîãäà ìàøèíà âûïîëíÿåò èíñòðóêöèþ ñ k ìåòêîé S , ìû ãîâîðèì, ÷òî ìàøèíà íàõîäèòñÿ â ñîñòîÿíèè k S . Èíñòðóêöèè áûâàþò òð¼õ òèïîâ: k I. S : R + +;S i II. Sk : R − −; S ;Si j III. Sk : STOP
  15. 15. Ïåðå÷èñëèìûå ìíîæåñòâà
  16. 16. Ïåðå÷èñëèìûå ìíîæåñòâà Îïðåäåëåíèå. Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì, åñëè ìîæíî íàïèñàòü ïðîãðàììó R äëÿ ðåãèñòðîâîé ìàøèíû, òàêóþ ÷òî a  îñòàíîâêà, åñëè a∈M R - - âå÷íàÿ ðàáîòà â ïðîòèâíîì ñëó÷àå
  17. 17. Ïåðå÷èñëèìûå ìíîæåñòâà Îïðåäåëåíèå. Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì, åñëè ìîæíî íàïèñàòü ïðîãðàììó R äëÿ ðåãèñòðîâîé ìàøèíû, òàêóþ ÷òî a  îñòàíîâêà, åñëè a∈M R - - âå÷íàÿ ðàáîòà â ïðîòèâíîì ñëó÷àå a Ïðè çàïóñêå ìàøèíû ÷èñëî ïîìåùåíî â ðåãèñòð R1, âñå îñòàëüíûå ðåãèñòðû ñîäåðæàò íóëè.
  18. 18. Ïðèìåð S1: R1−−; S2; S8 S2: R1−−; S3; S9 S3: R2++; S4 S4: R1−−; S5; S6 S5: R1−−; S3; S8 S6: R2−−; S7; S1 S7: R1++; S6 S8: R1++; S8 S9: STOP
  19. 19. Óðàâíåíèÿ ñ ïàðàìåòðàìè Ñåìåéñòâî äèîôàíòîâûõ óðàâíåíèé èìååò âèä M (a1, . . . , an , x1, . . . , xm ) = 0, ãäå M ìíîãî÷ëåí ñ öåëûìè êîýôôèöèåíòàìè, ïåðåìåííûå êîòîðãî ðàçäåëåíû íà äâå ãðóïïû:
  20. 20. Óðàâíåíèÿ ñ ïàðàìåòðàìè Ñåìåéñòâî äèîôàíòîâûõ óðàâíåíèé èìååò âèä M (a1, . . . , an , x1, . . . , xm ) = 0, ãäå M ìíîãî÷ëåí ñ öåëûìè êîýôôèöèåíòàìè, ïåðåìåííûå êîòîðãî ðàçäåëåíû íà äâå ãðóïïû: ïàðàìåòðû a1, . . . ,an ;
  21. 21. Óðàâíåíèÿ ñ ïàðàìåòðàìè Ñåìåéñòâî äèîôàíòîâûõ óðàâíåíèé èìååò âèä M (a1, . . . , an , x1, . . . , xm ) = 0, ãäå M ìíîãî÷ëåí ñ öåëûìè êîýôôèöèåíòàìè, ïåðåìåííûå êîòîðãî ðàçäåëåíû íà äâå ãðóïïû: ïàðàìåòðû a1, . . . ,an ; íåèçâåñòíûå x1, . . . ,xm . Ðàññìîòðèì ìíîæåñòâî M òàêîå, ÷òî a1 , . . . , an ∈ M ⇐⇒∃ x1 . . . xm {M (a1, . . . , an , x1, . . . , xm ) = 0}.
  22. 22. Óðàâíåíèÿ ñ ïàðàìåòðàìè Ñåìåéñòâî äèîôàíòîâûõ óðàâíåíèé èìååò âèä M (a1, . . . , an , x1, . . . , xm ) = 0, ãäå M ìíîãî÷ëåí ñ öåëûìè êîýôôèöèåíòàìè, ïåðåìåííûå êîòîðãî ðàçäåëåíû íà äâå ãðóïïû: ïàðàìåòðû a1, . . . ,an ; íåèçâåñòíûå x1, . . . ,xm . Ðàññìîòðèì ìíîæåñòâî M òàêîå, ÷òî a1 , . . . , an x1 . . . xm {M (a1, . . . , an , x1, . . . , xm ) = 0}. ∈ M ⇐⇒∃ Ìíîæåñòâà, èìåþùèå òàêèå ïðåäñòàâëåíèÿ íàçûâàþòñÿ äèîôàíòîâûìè.
  23. 23. Äèîôàíòîâû ìàøèíû Leonard Adleman è Kenneth Manders [1976] ââåëè ïîíÿòèå íåäåòåðìèíèðîâàííîé äèîôàíòîâîé ìàøèíû , NDDM .
  24. 24. Äèîôàíòîâû ìàøèíû Leonard Adleman è Kenneth Manders [1976] ââåëè ïîíÿòèå íåäåòåðìèíèðîâàííîé äèîôàíòîâîé ìàøèíû , NDDM . NDDM âõîä - óãàäàòü a P (a, x1, . . . , xm ) = 0 ? x1, . . . , xm ÄÀ ÍÅÒ a - ïðèíÿòü îòâåðãíóòü ?
  25. 25. Äèîôàíòîâû ìàøèíû Leonard Adleman è Kenneth Manders [1976] ââåëè ïîíÿòèå íåäåòåðìèíèðîâàííîé äèîôàíòîâîé ìàøèíû , NDDM . NDDM âõîä - óãàäàòü a P (a, x1, . . . , xm ) = 0 ? x1, . . . , xm ÄÀ ÍÅÒ a - ïðèíÿòü îòâåðãíóòü ? DPRM-òåîðåìà: NDDM èìååþò òàêóþ æå âû÷èñëèòåëüíóþ ñèëó êàê, íàïðèìåð, ìàøèíû Òüþðèíãà, òî åñòü ëþáîå ìíîæåñòâî, ïðèíèìàåìîå íåêîòîðîé ìàøèíîé Òüþðèíãà, ïðèíèìàåòñÿ íåêîòîðîé NDDM, è, î÷åâèäíî, íàîáîðîò.
  26. 26. Äèîôàíòîâà ñëîæíîñòü NDDM âõîä - óãàäàòü a P (a, x1, . . . , xm ) = 0 ? x1, . . . , xm ÄÀ ÍÅÒ a - ïðèíÿòü îòâåðãíóòü ?
  27. 27. Äèîôàíòîâà ñëîæíîñòü NDDM âõîä - óãàäàòü a P (a, x1, . . . , xm ) = 0 ? x1, . . . , xm ÄÀ ÍÅÒ a - ïðèíÿòü îòâåðãíóòü ? x SIZE(a)=ìèíèìàëüíî âîçìîæíîå çíà÷åíèå | 1 | + · · · + | m |, ãäå x x | | îáîçíà÷àåò äëèíó äâîè÷íîé çàïèñè . x
  28. 28. Äèîôàíòîâà ñëîæíîñòü Leonard Adleman è Kenneth Manders [1975] ââåëè â ðàññìîòðåíèå êëàññ D ñîñòîÿùèé èç ìíîæåñòâ M èìåþùèõ ïðåäñòàâëåíèÿ âèäà a ∈ M ⇐⇒ ⇐⇒ ∃x1 . . . xm P (a, x1 , . . . , xm ) = 0 |x1 | + · · · + |xm | ≤ |a|k .
  29. 29. Äèîôàíòîâà ñëîæíîñòü Leonard Adleman è Kenneth Manders [1975] ââåëè â ðàññìîòðåíèå êëàññ D ñîñòîÿùèé èç ìíîæåñòâ M èìåþùèõ ïðåäñòàâëåíèÿ âèäà a ∈ M ⇐⇒ ⇐⇒ ∃x1 . . . xm P (a, x1 , . . . , xm ) = 0 |x1 | + · · · + |xm | ≤ |a|k . ? Îòêðûòàÿ ïðîáëåìà. D = NP.
  30. 30. Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà) Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà). Êàæäîå ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿåòñÿ äèîôàíòîâûì.
  31. 31. Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà) Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà). Êàæäîå ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿåòñÿ äèîôàíòîâûì. Îïðåäåëåíèå. Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì , åñëè ìîæíî íàïèñàòü ïðîãðàììó R äëÿ ðåãèñòðîâîé ìàøèíû, òàêóþ ÷òî a  îñòàíîâêà, åñëè a∈M R - - âå÷íàÿ ðàáîòà â ïðîòèâíîì ñëó÷àå
  32. 32. Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà) Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà). Êàæäîå ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿåòñÿ äèîôàíòîâûì. Îïðåäåëåíèå. Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì , åñëè ìîæíî íàïèñàòü ïðîãðàììó R äëÿ ðåãèñòðîâîé ìàøèíû, òàêóþ ÷òî a  îñòàíîâêà, åñëè a∈M R - - âå÷íàÿ ðàáîòà â ïðîòèâíîì ñëó÷àå a Ïðè çàïóñêå ìàøèíû ÷èñëî ïîìåùåíî â ðåãèñòð R1, âñå îñòàëüíûå ðåãèñòðû ñîäåðæàò íóëè.
  33. 33. Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà) Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà). Êàæäîå ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿåòñÿ äèîôàíòîâûì. Îïðåäåëåíèå. Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì , åñëè ìîæíî íàïèñàòü ïðîãðàììó R äëÿ ðåãèñòðîâîé ìàøèíû, òàêóþ ÷òî a  îñòàíîâêà, åñëè a∈M R - - âå÷íàÿ ðàáîòà â ïðîòèâíîì ñëó÷àå a Ïðè çàïóñêå ìàøèíû ÷èñëî ïîìåùåíî â ðåãèñòð R1, âñå îñòàëüíûå ðåãèñòðû ñîäåðæàò íóëè. Áåç îãðàíè÷åíèÿ îáùíîñòè ìû ïðåäïîëàãàåì, ÷òî èìååòñÿ åäèíñòâåííàÿ êîìàíäà STOP êîìàíäà ñ ìåòêîé S m
  34. 34. Ãèïîòåçà Martin'a Davis'à (=DPRM-òåîðåìà) Ãèïîòåçà M. Davis'à (DPRM-òåîðåìà). Êàæäîå ïåðå÷èñëèìîå ìíîæåñòâî ÿâëÿåòñÿ äèîôàíòîâûì. Îïðåäåëåíèå. Ìíîæåñòâî M íàòóðàëüíûõ ÷èñåë íàçûâàåòñÿ ïåðå÷èñëèìûì , åñëè ìîæíî íàïèñàòü ïðîãðàììó R äëÿ ðåãèñòðîâîé ìàøèíû, òàêóþ ÷òî a  îñòàíîâêà, åñëè a∈M R - - âå÷íàÿ ðàáîòà â ïðîòèâíîì ñëó÷àå a Ïðè çàïóñêå ìàøèíû ÷èñëî ïîìåùåíî â ðåãèñòð R1, âñå îñòàëüíûå ðåãèñòðû ñîäåðæàò íóëè. Áåç îãðàíè÷åíèÿ îáùíîñòè ìû ïðåäïîëàãàåì, ÷òî èìååòñÿ åäèíñòâåííàÿ êîìàíäà STOP êîìàíäà ñ ìåòêîé S , à âm ìîìåíò îñòàíîâêè âñå ðåãèñòðû ïóñòû.
  35. 35. Ïðîòîêîë q ... t +1 t ... 0 S1 s1,q ... s1,t+1 s1,t ... s1,0 . . . . . . . . . . . . . . . . . . . . . Sk sk ,q ... sk ,t+1 sk ,t ... sk ,0 . . . . . . . . . . . . . . . . . . . . . Sm sm,q ...sm,t+1 sm,t . . . sm,0 1, åñëè íà øàãå t ìàøèíà áûëà â ñîñòîÿíèè k sk ,t = 0 â ïðîòèâíîì ñëó÷àå
  36. 36. Ïðîòîêîë q ... t +1 t ... 0 . . . . . . . . . . . . . . . . . . . . . S k sk , q ... sk ,t+1 sk ,t ... sk ,0 . . . . . . . . . . . . . . . . . . . . . R1 r1,q ... r1,t+1 r1,t ... r1,0 . . . . . . . . . . . . . . . . . . . . . R r ,q ... r ,t+1 r ,t ... r ,0 . . . . . . . . . . . . . . . . . . . . . Rn rn,q ... rn,t+1 rn,t ... rn,0 r ,t ýòî ñîäåðæèìîå -ãî ðåãèñòðà íà øàãå t
  37. 37. Ïðîòîêîë q ... t +1 t ... 0 . . . . . . . . . . . . . . . . . . . . . Sk sk ,q ... sk ,t+1 sk ,t ... sk ,0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R r ,q ... r ,t + 1 r , t ... r ,0 . . . . . . . . . . . . . . . . . . . . . Z1 z1,q ... z1,t+1 z1,t ... z1,0 . . . . . . . . . . . . . . . . . . . . . Z z ,q ... z ,t + 1 z ,t ... z ,0 . . . . . . . . . . . . . . . . . . . . . Zn zn,q . . . zn,t+1 zn,t . . . zn,0 z ,t = 0, âåñëè r ,t 0ñëó÷àå 1 ïðîòèâíîì
  38. 38. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP
  39. 39. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 =
  40. 40. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t
  41. 41. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t
  42. 42. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t
  43. 43. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t
  44. 44. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t
  45. 45. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t
  46. 46. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t
  47. 47. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 =
  48. 48. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t
  49. 49. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t
  50. 50. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t
  51. 51. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 =
  52. 52. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t
  53. 53. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 =
  54. 54. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t
  55. 55. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 =
  56. 56. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t
  57. 57. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t
  58. 58. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 =
  59. 59. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t
  60. 60. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 =
  61. 61. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t
  62. 62. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 =
  63. 63. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t
  64. 64. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t
  65. 65. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 =
  66. 66. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t
  67. 67. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 =
  68. 68. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t
  69. 69. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t
  70. 70. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t s9,t+1 =
  71. 71. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t s9,t+1 = (1 − z1,t )s2,t s1,0 =
  72. 72. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t s9,t+1 = (1 − z1,t )s2,t s1,0 = 1
  73. 73. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t s9,t+1 = (1 − z1,t )s2,t s1,0 = 1 s2,0 = · · · = sm,0 = 0
  74. 74. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t s9,t+1 = (1 − z1,t )s2,t s1,0 = 1 s2,0 = · · · = sm,0 = 0 r1,0 =
  75. 75. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t s9,t+1 = (1 − z1,t )s2,t s1,0 = 1 s2,0 = · · · = sm,0 = 0 r1,0 = a
  76. 76. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t s9,t+1 = (1 − z1,t )s2,t s1,0 = 1 s2,0 = · · · = sm,0 = 0 r1,0 = a r2,0 = · · · = rn,0 = 0 sm,q = 1
  77. 77. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t s9,t+1 = (1 − z1,t )s2,t s1,0 = 1 s2,0 = · · · = sm,0 = 0 r1,0 = a r2,0 = · · · = rn,0 = 0 sm,q = 1 s1,q = · · · = sm−1,q = 0
  78. 78. Ïðèìåð S1:R1−−; S2; S8 S4:R1−−; S5; S6 S7:R1++; S6 S2:R1−−; S3; S9 S5:R1−−; S3; S8 S8:R1++; S8 S3:R2++; S4 S6:R2−−; S7; S1 S9:STOP r1,t+1 = r1,t + s7,t + s8,t − z1,t s1,t − z1,t s2,t − z1,t s4,t − z1,t s5,t r2,t+1 = r2,t + s3,t − z2,t s6,t s1,t+1 = (1 − z2,t )s6,t s2,t+1 = z1,t s1,t s3,t+1 = z1,t s2,t + z1,t s5,t s4,t+1 = s3,t s5,t+1 = z1,t s4,t s6,t+1 = (1 − z4,t )s4,t + s7,t s7,t+1 = z2,t s6,t s8,t+1 = (1 − z1,t )s1,t + s8,t s9,t+1 = (1 − z1,t )s2,t s1,0 = 1 s2,0 = · · · = sm,0 = 0 r1,0 = a r2,0 = · · · = rn,0 = 0 sm,q = 1 s1,q = · · · = sm−1,q = 0 r1,q = · · · = rn,q = 0
  79. 79. Íîâûå çíà÷åíèÿ ðåãèñòðîâ r ,t + 1 = r ,t + + sk ,t − − z ,t sk ,t + ãäå -ñóììèðîâàíèå âåäåòñÿ ïî âñåì èíñòðóêöèÿì âèäà Sk : R + +; S , i − à -ñóììèðîâàíèå ïî âñåì èíñòðóêöèÿì âèäà Sk : R i j − −; S ; S .
  80. 80. Íîâûå ñîñòîÿíèÿ sd ,t+1 = d sk ,t + + d z ,t sk ,t + − d (1 − z ,t )sk ,t 0 + ãäå d -ñóììèðîâàíèå âåäåòñÿ ïî âñåì èíñòðóêöèÿì âèäà Sk : R + +; S ,d − d -ñóììèðîâàíèå âåäåòñÿ ïî âñåì èíñòðóêöèÿì âèäà Sk : R d j − −; S ; S , 0 à d -ñóììèðîâàíèå ïî âñåì èíñòðóêöèÿì âèäà Sk : R i d − −; S ; S .
  81. 81. Ïðîòîêîë q ... t +1 t ... 0 . . . . . . . . . . . . . . . . . . . . . Sk sk ,q ... sk ,t+1 sk ,t ... sk ,0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R r ,q ... r ,t + 1 r , t ... r ,0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z z ,q ... z ,t + 1 z , t ... z ,0 . . . . . . . . . . . . . . . . . . . . .
  82. 82. Ïðîòîêîë q ... t +1 t ... 0 . . . . . . . . . . . . . . . . . . . . . Sk sk ,q ... sk ,t+1 sk ,t ... sk ,0 sk = q s bt t = 0 k ,t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R r ,q ... r ,t + 1 r , t ... r ,0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z z ,q ... z ,t + 1 z , t ... z ,0 . . . . . . . . . . . . . . . . . . . . .
  83. 83. Ïðîòîêîë q ... t +1 t ... 0 . . . . . . . . . . . . . . . . . . . . . Sk sk ,q ... sk ,t+1 sk ,t ... sk ,0 s = k= q s bt t = 0 k ,t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R r ,q ... r ,t + 1 r , t ... r ,0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z z ,q ... z ,t + 1 z , t ... z ,0 . . . . . . . . . . . . . . . . . . . . .
  84. 84. Ïðîòîêîë q ... t +1 t ... 0 . . . . . . . . . . . . . . . . . . . . . Sk sk ,q ... sk ,t+1 sk ,t ... sk ,0 = k=s q s bt t = 0 k ,t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R r ,q ... r ,t + 1 r , t ... r ,0 = r = q r bt t = 0 ,t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z z ,q ... z ,t + 1 z , t ... z ,0 . . . . . . . . . . . . . . . . . . . . .
  85. 85. Ïðîòîêîë q ... t +1 t ... 0 . . . . . . . . . . . . . . . . . . . . . Sk sk ,q ... sk ,t+1 sk ,t ... sk ,0 = k=s q s bt t = 0 k ,t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R r ,q ... r ,t + 1 r , t ... r ,0 = r = q r bt t = 0 ,t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z z ,q ... z ,t + 1 z , t ... z ,0 = z = q z bt t =0 ,t . . . . . . . . . . . . . . . . . . . . .
  86. 86. Íîâûå çíà÷åíèÿ ðåãèñòðîâ q q q sk = sk ,t bt r = r ,t bt z = z ,t b t t =0 t =0 t =0 r ,t + 1 = r ,t + + sk ,t − − z ,t sk ,t
  87. 87. Íîâûå çíà÷åíèÿ ðåãèñòðîâ q q q sk = sk ,t bt r = r ,t bt z = z ,t b t t =0 t =0 t =0 r ,t + 1 = r ,t + + sk ,t − − z ,t sk ,t
  88. 88. Íîâûå çíà÷åíèÿ ðåãèñòðîâ q q q sk = sk ,t bt r = r ,t bt z = z ,t b t t =0 t =0 t =0 r ,t + 1 = r ,t + + sk ,t − − z ,t sk ,t
  89. 89. Íîâûå çíà÷åíèÿ ðåãèñòðîâ q q q sk = sk ,t bt r = r ,t bt z = z ,t b t t =0 t =0 t =0 r ,t + 1 = r ,t + + sk ,t − − z ,t sk ,t
  90. 90. Íîâûå çíà÷åíèÿ ðåãèñòðîâ q q q sk = sk ,t bt r = r ,t bt z = z ,t b t t =0 t =0 t =0 r ,t + 1 b t + 1 = r ,t b t + 1 + + sk ,t bt+1 − − z ,t sk ,t bt+1
  91. 91. Íîâûå çíà÷åíèÿ ðåãèñòðîâ q q q sk = sk ,t bt r = r ,t bt z = z ,t b t t =0 t =0 t =0 q −1 q −1 r ,t + 1 b t +1 = r ,t b t + 1 + + sk ,t bt+1 − − z ,t sk ,t bt+1 t =0 t =0
  92. 92. Íîâûå çíà÷åíèÿ ðåãèñòðîâ q q q sk = sk ,t bt r = r ,t bt z = z ,t b t t =0 t =0 t =0 q −1 q −1 r ,t + 1 b t +1 = r ,t b t + 1 + + sk ,t bt+1 − − z ,t sk ,t bt+1 t =0 t =0
  93. 93. Íîâûå çíà÷åíèÿ ðåãèñòðîâ q q q sk = sk ,t bt r = r ,t bt z = z ,t b t t =0 t =0 t =0 q −1 q −1 r ,t + 1 b t +1 = r ,t b t + 1 + + sk ,t bt+1 − − z ,t sk ,t bt+1 t =0 t =0 r − r ,0 = br + b + sk − b − z ∧ sk ) (
  94. 94. Íîâûå çíà÷åíèÿ ðåãèñòðîâ q q q sk = sk ,t bt r = r ,t bt z = z ,t b t t =0 t =0 t =0 q −1 q −1 r ,t + 1 b t +1 = r ,t b t + 1 + + sk ,t bt+1 − − z ,t sk ,t bt+1 t =0 t =0 r − r ,0 = br + b + sk − b − z ∧ sk ) ( r1 − a = br1 + b +sk − b − (z ∧ sk ) r = br + b +sk − b − (z ∧ sk ), = 2, . . . , n
  95. 95. Íîâûå ñîñòîÿíèÿ q q sk = sk ,t bt z = z ,t b t t =0 t =0 sd ,t+1 = d sk , t d z ,t sk ,t d (1 − z ,t )sk ,t + − 0 = + +
  96. 96. Íîâûå ñîñòîÿíèÿ q q sk = sk ,t bt z = z ,t b t t =0 t =0 sd ,t+1 = d sk , t d z ,t sk ,t d (1 − z ,t )sk ,t + − 0 = + +
  97. 97. Íîâûå ñîñòîÿíèÿ q q sk = sk ,t bt z = z ,t b t t =0 t =0 sd ,t+1 = d sk , t d z ,t sk ,t d (1 − z ,t )sk ,t + − 0 = + +
  98. 98. Íîâûå ñîñòîÿíèÿ q q sk = sk ,t bt z = z ,t b t t =0 t =0 sd ,t+1 = d sk , t d z ,t sk ,t d (1 − z ,t )sk ,t + − 0 = + +
  99. 99. Íîâûå ñîñòîÿíèÿ q q sk = sk ,t bt z = z ,t b t t =0 t =0 sd ,t+1bt+1 = d sk , t b d z ,t sk ,t b d (1 − z ,t )sk ,t b = + t +1 + − t +1 + 0 t +1
  100. 100. Íîâûå ñîñòîÿíèÿ q q sk = sk ,t bt z = z ,t b t t =0 t =0 q−1 sd ,t+1bt+1 = t =0 q −1 d sk , t b d z ,t sk ,t b d (1 − z ,t )sk ,t b = + t +1 + − t +1 + 0 t +1 t =0
  101. 101. Íîâûå ñîñòîÿíèÿ q q sk = sk ,t bt z = z ,t b t t =0 t =0 q−1 sd ,t+1bt+1 = t =0 q −1 d sk , t b d z ,t sk ,t b d (1 − z ,t )sk ,t b = + t +1 + − t +1 + 0 t +1 t =0
  102. 102. Íîâûå ñîñòîÿíèÿ q q sk = sk ,t bt z = z ,t b t t =0 t =0 q−1 sd ,t+1bt+1 = t =0 q −1 d sk , t b d z ,t sk ,t b d (1 − z ,t )sk ,t b = + t +1 + − t +1 + 0 t +1 t =0 sd − sd ,0 = b d sk + b d (z ∧ sk ) + b d ((e − z ) ∧ sk ) + + 0
  103. 103. Íîâûå ñîñòîÿíèÿ q q sk = sk ,t bt z = z ,t b t t =0 t =0 q−1 sd ,t+1bt+1 = t =0 q −1 d sk , t b d z ,t sk ,t b d (1 − z ,t )sk ,t b = + t +1 + − t +1 + 0 t +1 t =0 sd − sd ,0 = b d sk + b d (z ∧ sk ) + b d ((e − z ) ∧ sk ) + + 0 q−1 e= b 1 · t +1 = bq − 1 t =0 b−1
  104. 104. Èíäèêàòîðû íóëÿ z ,t = r 0, åñëè ,t = 0 1 â ïðîòèâíîì ñëó÷àå
  105. 105. Èíäèêàòîðû íóëÿ z ,t = r 0, åñëè ,t = 0 1 â ïðîòèâíîì ñëó÷àå b = 2 c +1 r ,t ≤ 2c − 1
  106. 106. Èíäèêàòîðû íóëÿ z ,t = r 0, åñëè ,t = 0 1 â ïðîòèâíîì ñëó÷àå b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1
  107. 107. Èíäèêàòîðû íóëÿ z ,t = r 0, åñëè ,t = 0 1 â ïðîòèâíîì ñëó÷àå b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t =
  108. 108. Èíäèêàòîðû íóëÿ z ,t = r 0, åñëè ,t = 0 1 â ïðîòèâíîì ñëó÷àå b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå
  109. 109. Èíäèêàòîðû íóëÿ z ,t = r 0, åñëè ,t = 0 1 â ïðîòèâíîì ñëó÷àå b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå 2c ∧ (2c − 1 + r ,t ) = 2c z ,t
  110. 110. Èíäèêàòîðû íóëÿ z ,t = r 0, åñëè ,t = 0 1 â ïðîòèâíîì ñëó÷àå b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå 2c ∧ (2c − 1 + r ,t ) = 2c z ,t q q (2c ∧ (2c − 1 + r ,t ))bt = 2c z ,t b t t =0 t =0
  111. 111. Èíäèêàòîðû íóëÿ z ,t = r 0, åñëè ,t = 0 1 â ïðîòèâíîì ñëó÷àå b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå 2c ∧ (2c − 1 + r ,t ) = 2c z ,t q q (2c ∧ (2c − 1 + r ,t ))bt = 2c z ,t b t t =0 t =0 q f f r 2c ∧ ((2c − 1) + ) = 2c z f= b 1 · t +1 = bq+1 − 1 t =0 b−1
  112. 112. Âûáîð c r ,t b
  113. 113. Âûáîð c r , t b = 2 c +1
  114. 114. Âûáîð c r , t b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå
  115. 115. Âûáîð c r , t b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå
  116. 116. Âûáîð c r , t b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå 2c ∧ r ,t =0
  117. 117. Âûáîð c r , t b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå 2c ∧ r ,t =0
  118. 118. Âûáîð c r , t b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå 2c ∧ r ,t =0
  119. 119. Âûáîð c r , t b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå q (2 c ∧ r ,t ) b t = 0 t =0
  120. 120. Âûáîð c r , t b = 2 c +1 r ,t ≤ 2c − 1 = 01 . . . 1 2c − 1 + r ,t = r 01 . . . 1, åñëè ,t = 0 1 ∗ · · · ∗ â ïðîòèâíîì ñëó÷àå q (2 c ∧ r ,t ) b t = 0 t =0 q f r 2c ∧ f= b 1 · t +1 = b q +1 − 1 =0 t =0 b−1
  121. 121. Âñå óñëîâèÿ
  122. 122. Âñå óñëîâèÿ b = 2 c +1
  123. 123. Âñå óñëîâèÿ b = 2 c +1 r − r ,0 = br + b + sk − b − ( z ∧ sk )
  124. 124. Âñå óñëîâèÿ b = 2 c +1 r − r ,0 = br + b + sk − b − ( z ∧ sk ) sd − sd ,0 = b d sk + b d (z ∧ sk ) + b d ((e − z ) ∧ sk ) + + 0
  125. 125. Âñå óñëîâèÿ b = 2 c +1 r − r ,0 = br + b + sk − b − ( z ∧ sk ) sd − sd ,0 = b d sk + b d (z ∧ sk ) + b d ((e − z ) ∧ sk ) + + 0 e = bb − 11 −q
  126. 126. Âñå óñëîâèÿ b = 2 c +1 r − r ,0 = br + b + sk − b − ( z ∧ sk ) sd − sd ,0 = b d sk + b d (z ∧ sk ) + b d ((e − z ) ∧ sk ) + + 0 e = bb − 11 −q z f = b b −− 1 q +1 f f r 2c ∧ ((2c − 1) + ) = 2c 1
  127. 127. Âñå óñëîâèÿ b = 2 c +1 r − r ,0 = br + b + sk − b − ( z ∧ sk ) sd − sd ,0 = b d sk + b d (z ∧ sk ) + b d ((e − z ) ∧ sk ) + + 0 e = bb − 11 −q z f = b b −− 1 q +1 f f r 2c ∧ ((2c − 1) + ) = 2c 1 f r 2c ∧ =0
  128. 128. Âñå óñëîâèÿ b = 2 c +1 r − r ,0 = br + b + sk − b − ( z ∧ sk ) sd − sd ,0 = b d sk + b d (z ∧ sk ) + b d ((e − z ) ∧ sk ) + + 0 e = bb − 11 −q z f = b b −− 1 q +1 f f r 2c ∧ ((2c − 1) + ) = 2c 1 f r 2c ∧ =0 sm = bq
  129. 129. Ïðîòîêîë q ... t +1 t ... 0 . . . . . . . . . . . . . . . . . . . . . Sk sk ,q ... sk ,t+1 sk ,t ... sk ,0 = k=s Q s bt t = 0 k ,t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R r ,q ... r ,t + 1 r , t ... r ,0 = r = Q r bt t = 0 ,t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z z ,q ... z ,t + 1 z , t ... z ,0 = z = Q z bt t =0 ,t . . . . . . . . . . . . . . . . . . . . .

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