      10. ⠢  ࠧ殬.

     10.1. ⥩訩 ਬ.

     10.1.1.  ᫥⥫쭮 ᨬ x[1]..x[n]. -
।,     騥   㣮 ᨬ "abcd".
(㣨 ᫮, ॡ ᭨,    ᫮ x[1]..x[n]
᫮ "abcd".)

    襭.  ਬ୮ n (᫨  , n-3) 権,
     室 ᪮ ᫮  室 ᫮.
   権  ஢, ⢨⥫쭮  ⠬  
室, ࠢ  ᨬ.    䥪⨢
ᯮᮡ.  ᫮ x[1]..x[n] ᫥ ࠢ,   -
  㪢  'a'.   ⮫쪮  ,     㪢
'b', ⥬ 'c', , , 'd'. ᫨   ࠢ뢠-
,  ᫮ "abcd" 㦥. ᫨  -  㦭  㪢
  ,  뢠  ࠧ⮣   稭 
᭠砫.

      ⮩     ࠧ ନ.  -
  ନ  ⠪  뢠  ⮬⮢, 
᪠,   ⥭ ᫮ x ᫥ ࠢ    
室       ᫥  ﭨ:  "砫쭮"  (0),
"ࠧ ᫥ a" (1), "ࠧ ᫥ ab" (2), "ࠧ ᫥ abc" (3)
  "ࠧ ᫥ abcd" (4).  । 㪢,  室 
᫥饥 ﭨ  ࠢ

         饥         ।      
         ﭨ       㪢          ﭨ
          0                a             1
          0              ஬ a         0
          1                b             2
          1                a             1
          1              ஬ a,b       0
          2                c             3
          2                a             1
          2              ஬ a,c       0
          3                d             4
          3                a             1
          3              ஬ a,d       0

 ⮫쪮    ﭨ 4,  ࠡ 稢.

     ⢥ ணࠬ 祢:
        i:=1; state:=0;
        {i - ࢠ ⠭ 㪢, state - ﭨ}
        while (i<> n+1) and (state <> 4) do begin
          if state = 0 then begin
            if x[i] = a then begin
              state:= 1;
            end else begin
              state:= 0;
            end;
          end else if state = 1 then begin
            if x[i] = b then begin
              state:= 2;
            end else if x[i] = a then begin
              state:= 1;
            end else begin
              state:= 0;
            end;
          end else if state = 2 then begin
            if x[i] = c then begin
              state:= 3;
            end else if x[i] = a then begin
              state:= 1;
            end else begin
              state:= 0;
            end;
          end else if state = 3 then begin
            if x[i] = d then begin
              state:= 4;
            end else if x[i] = a then begin
              state:= 1;
            end else begin
              state:= 0;
            end;
          end;
        end;
        answer := (state = 4);

     묨  ᫮,     ࠭ ଠ  ⮬,
 ᨬ쭮 砫 襣 ࠧ "abcd"   殬
⠭  .  (     "ﭨ",  ஬
諠 .)

     ନ,   ᯮ㥬, ⠪.  -  
᫥⥫쭮 ᨬ  ண 䨪஢  -
 ⢠.  ⢮ 뢠 䠢⮬,  
- 㪢. ᫨  ᪮쪮 㪢   ᫮, ⠭-
  㣮  ᫮, 뢠 砫 ࢮ.  ᫮ ⠪
⠥ ᢮ 砫.  ᫮ - ,   ⠭,  ᫨
  ᪮쪮    㪢.   ᫮ ⠥ ᢮
殬. ᫮ - ,  ⠭, ᫨  㪢    
砫,   . (㣨 ᫮, ᫮ -   砫,
,   , 砫 殢.)

       ନ  ⨢  㭪権 (. ࠧ 1.3) 
  ⠪: ᬮਬ 㭪  ᫮,   ਭ-
  祭 "⨭"  ""  ⨭  ᫮, 
"abcd"  ᢮ ᫮.  㭪   ⨢, 
 ⨢ ७

 x -> ᨬ쭮 砫 ᫮ abcd, 饣 殬 x

     10.2. ७  ࠧ - 筨 ஡.

     10.2.1.    । 㦤    ᫮
"abcd"  ந쭮 ᫮?

     襭. ,  ஡ 易  ⥬,   ࠧ 
 騥 㪢. ,  ਬ,    饬  宦
᫮  "ababc".   㪢 "a",    "b",  
 "a", ⥬ ᭮ "b".       ௥  
㪢  "c".  -  襬 ࠧ஢ -   -
 㣠 㪢,   ࠧ "ababc"    㦥.  
     ⥫ ਧ: ᫨  "c" 
㪢 "a",    ﭮ:      ᫥  㪢
"b"  "c",  ࠧ-⠪ 㤥 .

 ⨭,  ᪠:

 x   y   z   a   b   a   b   a   b   c   ....  <- 室 ᫮

             a   b   a   b   c       <-    ࠧ 

                     a   b   a   b   c  <-     

 ࠧ,  
                           |
 x   y   z   a   b   a   b |             <- 室 ᫮
                           |
             a   b   a   b | c       <-    ࠧ 
                           |
                     a   b | a   b   c  <-     
                           |
    ࠧ,    
஢થ.    -०      ⮬,
騩  室  ᫮ 㪢  㪢  室騩  -
ﭨ  ﭨ  ᨬ  ⠭ 㪢.

     10.2.2.  ﭨ ᮮ⢥饣 ⮬   ⠡-
  室 ( ﭨ  ᨬ  ண  -
 㪢).

     襭. -० ﭨ    ᮮ⢥⢮  -
襬  砫  ࠧ, 饬 殬 ⠭ 
᫮.  㤥 : 0,  1  ("a"),  2  ("ab"),  3  ("aba"),  4
("abab"), 5 ("ababc").  室:

         饥         ।      
         ﭨ       㪢          ﭨ
          0                a             1 (a)
          0              ஬ a         0
          1 (a)            b             2 (ab)
          1 (a)            a             1 (a)
          1 (a)          ஬ a,b       0
          2 (ab)           a             3 (aba)
          2 (ab)         ஬ a         0
          3 (aba)          b             4 (abab)
          3 (aba)          a             1 (a)
          3 (aba)        ஬ a,b       0
          4 (abab)         c             5 (ababc)
          4 (abab)         a             3 (aba)
          4 (abab)       ஬ a,c       0

 ஢ન ᬮਬ,  ਬ,   ᭨ ப.  ᫨
⠭    砫  "abab",  ⥬  㪢
"a",  ⥯  ⠭    砥    "ababa".  -
襥  砫  ࠧ ("ababc"), ஥    - 
"aba".

     ᪨ :  ਫ,   㤭  ⮨  
⮬,     ᪮쪮   ࠧ,  
   ⨭.  ᮮ⢥ ᪮쪮 -
砫 ࠧ,  栬 室 ᫮.    -
⮬   ᠬ   .   ⠫?

     ᪨ ⢥.   ⮬,  ᠬ    -
।   ⠫ -   , ६ 騥
 砫.

      ⠢ 㤠   ⭮ ࠧ 
ணࠬ,  ⢫   ⮣ ࠧ ᠭ ᯮ-
.   ⥫   ணࠬ,   ந-
 ࠧ  ந쭮 ᫮.         
⠯:  ᭠砫   ࠧ ந ⠡ 室 筮
⮬,  ⥬ ⠥ 室 ᫮  ﭨ  ८ࠧ-
    ᮮ⢥⢨   ⮩ ⠡楩.  ⮤  -
   ᫮  ᪠ (.  ),    
᪠ ᫮   ⮩  䥪⨢ ,
뢠  ⬮    -  - .  ० 
  ᯮ⥫ ⢥ত.

     10.3. ᯮ⥫ ⢥ত

      ந쭮 ᫮ X ᬮਬ   砫, -
६  騥  栬,  롥६   ᠬ .
( , 筮, ᠬ ᫮ X.) 㤥   n(X).

     ਬ: n(aba)=a, n(abab)=ab, n(ababa)=aba, n(abc) =  -
⮥ ᫮.

     10.3.1. ,   ᫮ n(X), n(n(X)), n(n(n(X)))
 ..  砫 ᫮ X.

     襭.     (ᮣ᭮ ।)  -
砫 ।饣.

      ⮩  稭    栬 ᫮ X.

     10.3.2. ,  ᫥⥫쭮 ।饩  
뢠 ( ⮬ ᫮).

     襭.  ᫮  ।饣.

     .  ,   ᫮, ६ 饥
砫  殬 ᫮ X (஬ ᠬ X)  室    ᫥-
⥫쭮 n(X), n(n(X)),...

     襭.  ᫮ Y  ६ 砫    X.
  n(X)  - ᠬ   ⠪ ᫮, ⠪  Y  
n(X).   ᫮  砫 X, ⮬   ⪮
   砫  : Y  砫 n(X). -
筮, Y   n(X). 㦤  樨,  ।-
,  ⢥ত  ୮   ᫮   X,  
⭮,   ᫮ n(X).   ᫮ Y, 饥 殬 
砫  n(X),  ࠢ n(X),  室  ᫥⥫쭮
n(n(X)), n(n(n(X))), ...,   ॡ .

     10.4.   -  - 

       -  -  ()  砥    室
᫮

        X = x[1]x[2]...x[n]

 ᬠਢ  ᫥ ࠢ 㪢  㪢,   
⮬ ᨢ ࠫ ᥫ l[1]..l[n], ⠪ 

      l[i] =  ᫮ n(x[1]...x[i])

(㭪  n  ।  ।饬 㭪). : l[i] 
 襣 砫 ᫮ x[1]..x[i], ६ -
  殬.

     10.4.1.    ⭮襭       ᫮?
㣨 ᫮,  ᯮ짮      ।
⮣,   ᫮ A ᫮ ᫮ B?

     襭.  ਬ    ᫮ A#B,  # - ᯥ-
쭠 㪢,     A,   B.  A  
᫮ ᫮ B ⮣  ⮫쪮 ⮣,  । ᥫ  -
ᨢ l 㤥 ᫮, ࠢ  ᫮ A.

     10.4.2.    ⠡ l[1]..l[n].

     襭.  ।,   i 祭 l[1]..l[i] 㦥
.  ⠥ । 㪢 ᫮ (.. x[i+1])   
᫨ l[i+1].

     1                                              i   i+1
    --------------------------------------------------------
    |           㦥 ⠭  X                |   |
    --------------------------------------------------------
    \-----------Z-----------/    \------------Z------------/


㣨 ᫮,   砫 Z ᫮ x[1]..x[i+1], -
६ 騥  栬 -       -
 . 㤠   砫?    砥
  ண ᫮ Z' ਯ뢠 㪢 x[i+1].  Z' -
 砫  殬 ᫮ x[1]..x[i].    ᫮,
饥 砫  殬 ᫮ x[1]..x[i],    -  ,
⮡   ᫥ 㪢 x[i+1].

     砥 ⠪ 楯 ᪠ ᫮ Z. ᬮਬ  -
砫 ᫮ x[1]..x[i], 騥 ६   栬.  
  롥६  室騥 - ,  묨  㪢 x[i+1]. 
室 롥६ ᠬ . ਯᠢ      x[i+1],
稬 ᪮ ᫮ Z.

       ᯮ짮 ᤥ묨  ਣ⮢ﬨ
  ᯮ,    ᫮, 騥 ६ 砫 
栬  ᫮,   묨 ਬﬨ  
 㭪樨 n  ।饣 ࠧ.   砥:

    i:=1; l[1]:= 0;
    {⠡ l[1]..l[i]  ࠢ쭮}
    while i <> n do begin
    | len := l[i]
    | {len -  砫 ᫮ x[1]..x[i], ஥  
    |     殬;    砫 
    |    室騬}
    | while (x[len+1] <> x[i+1]) and (len > 0) do begin
    | | {砫  室騬, ਬ塞   n}
    | | len := l[len];
    | end;
    | {諨 室饥  㡥  ⢨}
    | if x[len+1] = x[i+1] do begin
    | | {x[1]..x[len] - ᠬ  室饥 砫}
    | | l[i+1] := len+1;
    | end else begin
    | | {室 }
    | | l[i+1] := 0;
    | end;
    | i := i+1;
    end;

     10.4.3. ,  ᫮ ⢨   ਢ  ⮫쪮
 ⬥  ॢ室 Cn  ன ⠭ C.

     襭.    祢: ࠡ⪠  ।
㪢  ॡ  権  ७ 横. -
  ⠪  㬥蠥 len  ࠩ   1, 
 ⮬ 砥 l[i+1]  ⭮  l[i].  㣮 -
஭,  㢥祭 i   稭 l[i]    
  祬  1, ⠪    ᨫ쭮 뢠    -
 뢠  㤥 ᪮஢ ⠭.
      筮,   ࠢ⢮
    l[i+1] <= l[i] - (᫮ 権  i- 蠣) + 1

    (᫮ 権  i- 蠣) <= l[i] - l[i+1] + 1
 ⠥ ᫮  ࠢ⢠  ᥬ i      業
ᢥ  饣 ᫠ 権.

     10.4.4.  㤥  ᯮ짮  , ⮡ ᭨,
  ᫮ X  n ᫮ ᫮ Y  m. (  
    ᯥ樠쭮 ࠧ⥫ #, ᠭ .) 
⮬ ᫮ ⢨ 㤥   C*(n+m),   ᯮ㥬  -
  ⮦. ਤ㬠,      Cn ( -
  ⢥ , ᫨ ᪮  ࠧ  ⪨,  
᫮,  ஬   - ).

     襭.  ਬ塞     ᫮ A#B.  ⮬ -
᫥ 祭 l[1],...,l[n] ஢  ᫮ X   m  
    祭.    ⮫쪮 祭 l[i]
 ⥪饣 i - ஬   ஬ ⠡ l[1]..l[n],   
᫥ 祣  㦭.

      ࠪ⨪ ᫮ X  Y   室 , ⮬
ᬮ  ᫮  X  ⥬ ᫮ Y 㤮 ନ   ࠧ
横.   ⠪  嫮  ࠧ⥫.

     10.4.5.  ᮮ⢥騩  (஢騩, -
  ᫮ X=x[1]..x[n] ᫮ ᫮ Y=y[1]..y[m]).

     襭. 砫 塞 ⠡ l[1]..l[n]    ࠭.
⥬ 襬 ⠪ ணࠬ:
     j:=0; len:=0
     {len -  ᨬ쭮 砫 ᫮ X, ६
            饣 殬 ᫮ y[1]..j[j]}
     while (len <> n) and (j <> m) do begin
     | while (x[len+1] <> y[j+1]) and (len > 0) do begin
     | | {砫  室騬, ਬ塞   n}
     | | len := l[len];
     | end;
     | {諨 室饥  㡥  ⢨}
     | if x[len+1] = y[j+1] do begin
     | | {x[1]..x[len] - ᠬ  室饥 砫}
     | | len := len+1;
     | end else begin
     | | {室 }
     | | len := 0;
     | end;
     | i := i+1;
     end;
     {᫨ len=n, ᫮ X ⨫;   諨  
        ᫮ Y, ⠪   ⨢ X}

     10.5.   - 

        ,        -
:    ⨯筮  樨  ⠥   
 㪢 ᫮,  ஬   ࠧ.  ⠪  -
  ?  . , ਬ,  饬 ࠧ "abcd".
ᬮਬ  ⢥ 㪢 ᫮: ᫨,  ਬ,    㪢
"e",       室    㪢. (
ᠬ ,  ࠧ 㪢 "e" , ⮬     
 ࠭ ⮩ 㪢.)

      ਢ ᠬ ⮩ ਠ ⮣ ⬠,  
  ࠭ ன ࠡ   .  x[1]..x[n]
- ࠧ,   ᪠.   ᨬ s  -
 ࠢ  宦  ᫮ X,    襥  k,  
஬ x[k]=s.  ᢥ 㤥 ࠭  ᨢ pos[s]; -
  ᨬ  s   砥,   㤥 㤮 
pos[s] = 0 ( 㢨 , 祬).

     10.5.1.   ᨢ pos?

     襭.
          pos[s] ࠢ묨 0
        for i:=1 to n do begin
          pos[x[i]]:=i;
        end;

   ᪠  㤥 ࠭  ६ last  㪢
 ᫮, ⨢ ன ᫥ 㪢 ࠧ. 砫 last = m
( ࠧ), ⥬ ⥯ 㢥稢.

     last:=m;
     { ।騥  ࠧ 㦥 ஢७}
     while last <= m do begin {᫮  稫}
     | if x[m] <> y[last] then begin {᫥ 㪢 ࠧ}
     | | last := last + (m - pos[y[last]]);
     | | {m - pos[y[last]]  -   ᤢ ࠧ,
     | |     ஬ ⨢ y[last] ⠭ ⠪ 
     | |    㪢  ࠧ. ᫨ ⠪ 㪢  ,
     | |     ᤢ    ࠧ}
     | end else begin
     | | ᫨ 뭥譥  室, .. ᫨
     | | x[1]..x[m] = y[last-m+1]..y[last],
     | |  ᮮ  ᮢ;
     | | last := last+1;
     | end;
     end;

⮪ ४ ஢ ᮢ ஢ ࠢ ,
.. 稭  ᫥ 㪢 ࠧ ( ன ᮢ -
 ).  ⠪  , ந  -
 ࠭  ࠭  pos[s],  m-pos[s], .. ᫮ 㪢  -
ࠧ ࠢ  ᫥ 宦 㪢 s.

      ࠧ 䨪樨 ⮣ ⬠. ਬ, -
 ப last:=last+1   last:=last+(m-u),  u - -
न ண ࠢ 宦 㪢 x[m]   ࠧ.

     10.5.2.   ᥣ    ணࠬ?

     襭.  ஥ ⠡ pos 
        for i:=1 to n-1 do...
 ᭮ ணࠬ  last:=last+1 
        last:= last+m-pos[y[last]];


     ਢ  饭 ਠ ⬠  - 
   ॡ ⢥  n ⢨ (᫮
⢨  浪  mn),  ந뢠    -  -
.


     10.5.3. ਢ ਬ 樨,  ன ࠧ  -
  ᫮,   ॡ 浪 mn ⢨,  ⮡
 ⠭.

     襭.  ࠧ    baaa..aa,    ᠬ  ᫮
⮨  ⮫쪮    㪢 a.    蠣 ᮮ⢥⢨
   ᫥ .


     騩 ( 饭)   -  ࠭-
,  ᫮ ⢨  ࢮ室 C*(m+n)  襬 砥. 
ᯮ  ,       ⬠  -  -
. ।⠢ ᥡ,   ࠢ  ࠧ    室
᫮,  ࠢ .  ⮬  ᮪ Z (騩-
  殬 ࠧ) ᮢ,  ⥬ 㦨 ࠧ稥: ।
Z  ࠧ ⮨  ,   室 ᫮.   ᪠
    室 ᫮?   㦥 ࠣ,  ࠢ
Z,   ।  ⮨   㪢,   ࠧ.  ଠ
  ᤢ ࠧ  ᪮쪮 権 ࠢ 
᪠ ய  宦.  ᤠ ᫥ ᫨ -
࠭    Z 襣 ࠧ.     ⮪,
    (᫥  ⠡  ᤢ  ᯮ짮 ) 
㫮  C*(m+n) ⢨.

     10.6.  

       ᭮  ⮩ . ।⠢ ᥡ, 
 ᫮  m  饬 ࠧ  n. ० 窮 ࠧ-
  n   㤥    室 ᫮.  , 
ᮢ  ᫮  窥   ࠧ殬. ࠢ 
㪢 .  ⮣ 䨪㥬  㭪  ᫮
 n. ᫨ 祭 ⮩ 㭪樨  ᫮  窥   -
ࠧ ࠧ,  ᮢ . 쪮 ᫨ 祭 -
, 㦭 ஢ ᮢ  㪢.

       먣뢠  ⠪ 室?  , 祣  -
  ⮡  ᫨ 祭 㭪樨  ᫮  窥, 
ࠢ 㦭   㪢 ⮣ ᫮.     -
 ࠢ  ࠧ殬.    먣 ,    
  祣.    ᤢ 窠 ᫮   , 
  㪢    㡨ࠥ  砫.   ,
⮡  ⨬   뫮   ,  -
 㭪.

     10.6.1. ਢ ਬ 㤮  ᫥ 㭪樨.

     襭.   㪢  ᫮  ࠧ    ࠬ,
।⠢騬  ᮡ 楫 ᫠.  㤮 㭪樥 -
 㬬 . ( ᤢ 窠 㦭   ᫮
  ய襥.)

       㭪樨  ᫮,    ਬ-
 .  㣠 㭪  ⮬ 砥  ࠡ -
.  :    㭪権   砫 ࠡ
⬠ 롨   砩. ( ࠣ, 騩 -
 襬 ,  㤥 ,      㭪樥
 .)

     10.6.2. ਢ ਬ ᥬ⢠ 㤮 㭪権.

     襭.  롥६  ஥  ᫮  p (⥫쭮 ⮥,
ᬮ )    x   p.  ᫮ -
 n 㤥 ᬠਢ  ᫥⥫쭮 楫 ᥫ (-
 㪢 ).  ᫠ 㤥 ᬠਢ  -
 童 ⥯ n-1  ᫨ 祭 ⮣ 童
  p  窥 x.   㤥      㭪権  ᥬ⢠
(   p  x 砥, ⠪ ࠧ, ᢮ 㭪).
  誠  1 ᮮ⢥ ⠭ 襣 童, 㬭-
  x   ᢮ 童.
     饥 ᮮࠦ    ⮣,  ᮢ
 ᫨誮 .  ᫮ p 䨪஢   ⮬  -
⮥,    X    Y  -   ࠧ ᫮  n.   ᮮ-
 ࠧ 童 ( ।,     
㪢  ࠧ  -    p, 襬 ᫠ 㪢 䠢-
).  祭 㭪樨 砥,   窥 x  
ࠧ 童 ᮢ,    ࠧ 頥 
0.   童 ⥯ n-1     n-1 -
.  ࠧ, ᫨ n   p,  砩 x  
蠭ᮢ   㤠 .


     10.7.  ᫮ ࠧ  ⮬

       ᪠  ⭮ ᫮,    ᫮  
.  ਬ,  ᪠ ᫮  a?b,   ? 
  㪢 (묨 ᫮,     㪢  b  
ﭨ 2 ᫥ 㪢 a).

     10.7.1      ⮬, ஢騩,   
室 ᫮ ࠣ  a?b.

     襭.    ᫮, ᫥ ,   㪢 a 
᫥    ।᫥ -     ⨬  ᪮
ࠣ. 砥 ⠪ ⮬:

    ஥ ﭨ    । 㪢    ﭨ

       00                     a                 01
       00                   a                 01
       01                     a                 11
       01                   a                 10
       10                     a                 01
       10                     b                 
       10                 a   b            00
       11                     a                 11
       11                     b                 
       11                 a   b            10


     㣮 ⠭   ࠧ -  窠  (*),  
  ன   ⠢  ᫮. ਬ, -
ࠧ ab*cd 砥,   饬 ᫮ ab,   ᫥-
  㣮,  ⥬ (  ﭨ) ᫥ cd.

     10.7.2.   ⮬, ஢騩,     
室 ᫮ ࠧ ab*cd ( ᠭ ⮫쪮  ᫥).

     襭.

    ஥ ﭨ    । 㪢    ﭨ

                           a                 a
                         a                 
        a                     b                 ab
        a                     a                 a
        a                   a   b          
        ab                    c                 abc
        ab                  c                 ab
        abc                   d                 
        abc                   c                 abc
        abc                    d          ab

        ᪠ -     ᫮  ண
ᯨ᪠.

     10.7.3.    ᯨ᮪  ᫮ X[1],...,X[k]  ᫮ Y. ।-
, 室      ᫮ X[i]  ᫮ Y ( ᫮-
). ⢮ ⢨   ॢ室 ⠭, 㬭-
  㬬   ᫮ ( ᯨ᪠  ⮣,  ஬
ந室 ).

     襭. 祢 ᯮᮡ ⮨  ⮬, ⮡  ᫮
  ᯨ᪠ ஢ ⤥쭮 (    ᬮ७
⬮).   ⮬   㪫뢠   ᫮
⢨ (- 㬭 k   ᫮ Y).

     ᬮਬ     㣮  ஭.    ࠧ  
ᯨ᪠ ᮮ⢥  ⮬   ⢮ -
ﭨ.   ꥤ   ⮬, ⢮ ﭨ
ண 㤥 ந  ﭨ    ⮬-
⮢.    -  祭  讥  ⢮.      ᠬ 
設⢮  ⮢ 㯭  (      
⥭ 室 ᫮)    ⮣ 砥 . -
୮   (   )   㤥 ᯮ짮.

     ᯮ      -  - .  , 
室 ᫮,  ࠭ 襥 砫 ࠧ,  饥
殬 ⠭ .   ᫥ ࠭  
 ࠧ殢 襥  砫, 饥 殬 ⠭
.  騬 뢠 ⠪ 砭: 筮 ࠭
ᠬ    -  ⠫     ⠭
( 訥 砫 ࠧ殢, 騥  栬).

         ࠧ  ॢ, ꥤ  ᮢ騥 -
砫 ⪨. ਬ,  ࠧ殢

      {aaa, aab, abab}

ᮮ⢥ ॢ

                       a/ *
           a     a    / b
        * --- * --- * --- *
                \b     a     b
                  \ * --- * --- *

ଠ쭮 , 設 ॢ   砫   -
ࠧ殢,  뭮 設  ਯ뢠 㪢.

  室 ᫮,    ⮬ ॢ: ⥪ -
設 -   (ᠬ ࠢ)  設,   -
殬  ⠭  (=訩  ⠭ , -
騩 砫   ࠧ殢).

। 㭪 n, 㬥⠬  祭ﬨ  ன  
設  ॢ. , n(P) =  設 ॢ, -
 殬 P. (, 設 ॢ -  ᫮.)  -
 ⠪ ⢥ত:

     10.7.4.  P - 設 ॢ. ,    ⢮
 設,  栬 P, ࠢ {n(P), n(n(P)),...}

     襭.  .  ⥫⢮  筮 ⢥ত 
⬠  -  - .

      ᭮,  㦭 , 室  設 P  
㪢 y 室 ᫮.  ᬠਢ ᫥⥫쭮  -
設  P, n(P), n(n(P))  ..,   㦨 ⠪,  -
ன 室 ५  㪢 y.    設,      
५ ,  㤥 訬 ᫥騬 .

     ⠥  ,      設 ॢ ᫨
㪠⥫  祭 㭪樨 n  ⮩ 設.   
࠭,  ⮬ 祭 n   ⪨ ᫮ ᯮ
 ᫥ । 祭 㭪樨 n.  砥,  
設  ॢ  ᫥  ᬠਢ  浪 ⠭ 
. 㤭 ,      㫮    ॡ㥬
᫮ ⢨ ( ⠭   ᫠ 㪢    䠢-
).  ⭮騥   ⮬ ஡ .    ⬠
 .

      ᮢ,  ᢮⢠ ᫮  ᯮ-
    ⮬⮢. 뢠,    
 뢠  ࠧ殢, 騩  ⠪ ᢮⢠ -
 ॣ ࠦ.

     ।.    䨪஢  䠢 ,  -
ঠ騩  ᨬ  'l', 'e', '(', ')', '*'  '|' (  -
짮  ஥ ॣ ࠦ    -
६訢  㪢).  ࠦ    ⠪
ࠢ:

     () 㪢 䠢  - ॣ୮ ࠦ;
     () ᨬ 'l', 'e' - ॣ ࠦ;
     ()  ᫨ A,B,C,..,E - ॣ ࠦ,  (ABC...E) -
          ॣ୮ ࠦ.
     ()   ᫨   A,B,C,..,E   -   ॣ   ࠦ,    
          (A|B|C|...|E) - ॣ୮ ࠦ.
     () ᫨ A - ॣ୮ ࠦ,  A* - ॣ୮ -
          .

  ॣ୮  ࠦ  ⢮ ᫮  䠢 
 ⠪ ࠢ:

     () 㪢 ᮮ⢥ ⭮ ⢮, 饥
          㪢 ᫮, 饣  ⮩ 㪢;
     ()  ᨬ  'e' ᮮ⢥ ⮥ ⢮,  ᨬ
         'l' - ⭮ ⢮, ⢥  ⮬
         ண  ⮥ ᫮;
     () ॣ୮ ࠦ (ABC...E) ᮮ⢥ ⢮
          ᫮,   , ᫨   ᫮    A
         ਯ ᫮  B, ⥬  C,..., ⥬  E ("-
         ⥭" );
     ()   ॣ୮   ࠦ  (A|B|C|...|E)  ᮮ⢥
         ꥤ   ,   ᮮ⢥    ࠦ
         A,B,C,..,E;
     () ॣ୮ ࠦ A* ᮮ⢥ ""  -
         ⢠, ᮮ⢥饣 ࠦ A,   ⢮
           ᫮,     ⠪ ࠧ१  ᪨, 
          ᮪  ਭ  ,  ᮮ⢥饬
         ࠦ  A.  ( ⭮, ⮥ ᫮ ᥣ ᮤ-
           A*.)

     ਬ

ࠦ               ⢮

(a|b)*                   ᫮  㪢 a  b
(aa)*                    ᫮  ⭮ ᫠ 㪢 a
(l|a|b|aa|ab|ba|bb)      ᫮    祬 2 㪢 a,b

     10.7.5.     ॣ୮  ࠦ,  ஬  ᮮ-
 ⢮  ᫮  㪢 a   b,      ᫮
㪢 a ⭮.

     襭. ࠦ b*   ᫮  a,  ࠦ
               (b* a b* a b*)
-  ᫮ ஢   㪢  a.  ⠥  ꥤ  
⢠,  ⮬ ਬ :
              ((b* a b* a b*) | b*)*

     10.7.6.   ॣ୮ ࠦ, ஥  -
⢮  ᫮  㪢 a,b,c,     ᫮  bac  
᫮.

     襭. ((a|b|c)* bac (a|b|c)*)

        ᪥ ࠧ  ᫮  㫨-
 ⠪:  ஢,  ਭ    ᫮  ,  ᮮ-
饬  ॣ୮ ࠦ.

     10.7.7.  ࠦ ᮮ⢥ ࠧ栬 a?b  ab*cd,
ᬮ७  ࠭? ( ࠧ '*' ᯮ   ⮬ -
,   ॣ ࠦ!) ।,  䠢  -
ন 㪢 a,b,c,d,e.

     襭. ((a|b|c|d|e)* a (a|b|c|d|e) b (a|b|c|d|e)*)  
              ((a|b|c|d|e)* ab (a|b|c|d|e)* cd (a|b|c|d|e)*).

     10.7.8.  ,      类 ॣ୮ ࠦ
  ந    ⮬,    ᯮ  ᮮ-
饥 ⮬ ࠦ ⢮ ᫮.

     襭.  ॡ  ⨥ - ⨥  筨
(  ନ஢  筮 ⮬). ।⠢ ᥡ
ਥ஢  - ⨭  ᪮쪨 祪  (設)  
 ५, ᮥ  窨 (ॡ).   -
 ॡ ᠭ 㪢 ( 易⥫쭮  ).  ⠪-
  ।  設  ࠭  - 砫쭠   筠 . 
⨭ 뢠 筨.

     㤥  ࠧ묨 ᯮᮡ    ,   㪢
  ண  (  ५,   ).     
, ⠪ ࠧ, ᮮ⢥ ஥ ᫮.   筨  
楫  ᮮ⢥  ⢮  ᫮  -  ᫮,  
      .

     砭. ᫨ ᮢ ﭨ 筮  ⮬  
  祪,   室  ⥭ 㪢 ࠧ   -
,  ⠭ ᭮,   ⮬ -     砩
筨.

       㤥 ந  ⮬  ॣ୮ ࠦ
  ਥ.  砫    ந  筨,  ஬  ᮮ-
      ᠬ ⢮ ᫮. ⥬  ந쭮
筨 ந ⮬,   ஢,  ਭ  
᫮ ᮮ⢥饬 .

     10.7.9.   ॣ୮ ࠦ ந 筨, -
騩   ⢮.

     襭.   ஥ ॣ୮ ࠦ. -
 ᮮ⢥    ५. ꥤ ॠ-
 ⠪:

               |---------|
          ---->|*1   1*|->---
        /      |---------|      \
      /         |---------|       \
    * --------->|*2   2*|--->-----* 
      \        |---------|        /
         \     |---------|       /
           --->|*3   3*|--->--
               |---------|

ᮢ  ⨭    ꥤ    ,  אַ-
㣮쭨 -  筨, ᮮ⢥騥 ; 㪠 砫
  設.   ५ ( 6) 㪢  ᠭ.

     ⥭樨 ᮮ⢥ ⨭

       |--------|         |--------|          |--------|
 *--->|*1  1*|---->----|*2  2*| ---->----|*3  3*|-->--*
       |--------|         |--------|          |--------|

     , 樨 ᮮ⢥ ⨭

    *--------->----------*----------->----------*
                        /   \
                      /       \
                      |       |
                      V       ^
                      |       |
                    -------------
                    | *1   1* |
                    -------------

     10.7.10.  筨. ந  ⮬, ஢-
騩, ਭ  室 ᫮  ,  ᮮ⢥饬
筨 (..     ᫮,     ).

     襭. ﭨﬨ ⮬  ⢠ 設 -
. ,  ஥ 砫 X 室 ᫮,  㤥
  ⢮  設 筨,    ன
 砫쭮, ⠢   ᫮ X.

     뢠,  ॣ ࠦ, ⮬  筨
ᯮ     ⢠. ⮡ 㡥   ⮬,  
⠫  ⠪ :

     10.7.11.   筨. ந ॣ୮ ࠦ, -
饥   ⢮,    筨.

     襭.  (饭  ⭨  ᥬ    .)
 筨  設 1..k. 㤥 ,   1  -  
砫,    k  - . १ D[i,j, s] 稬 ⢮ 
᫮,       i  j, ᫨    ⢥
஬  㭪⮢  ࠧ蠥  ᯮ짮 ⮫쪮 設
1,...,s. ᭮ ।, 筨 ᮮ⢥ ⢮
D[1,k,k].
     樥   s 㤥 뢠 ॣ୮  
D[i,j,s]   i  j.   s=0    祢  (஬
設  饭, ⮬    ⮨ ⮫쪮 
㪢).
      祣 ⮨ ⢮ D[i,j,s+1]? ⬥⨬     -
,    室  s+1- 設.  ⮬  ࠧ-
    ,    㦥  室  . -
⮬  ᮮࠧ, 

 D[i,j,s+1] = (D[i,j,s]| (D[i,s+1,s] D[s+1,s+1,s]* D[s+1,j,s]))

(쭮 :  ᯮ㥬   権    ⢠
祭     ॣ ࠦ). ⠥ ᯮ짮-
 । 樨.

     10.7.12.   ᯮ   ᠬ 㦤?

     ⢥.  ⬥  ᫥ 業 砩襣 ,
.  9 (   ).

     10.7.13. ,   ,   ॣ-
묨  ࠦﬨ,      ,  ᫨   ࠧ訫 -
짮  ⮫쪮 ꥤ,     栭  (  ᫥-
⥫쭮,  祭 -  ࠦ १ ꥤ  -
栭).

     襭.  ⮬⮢ 室  栭 祢.

     砭.    ࠪ⨪  ஫ ࠥ ᫮ ﭨ
⮬. 뢠,     ⠪ ,    室  
筨   ⮬ ॡ ᯮ樠쭮  ᫠ -
ﭨ.  ஡ ᬮ७ 易  ⨬ ⥮᪨ 
ࠪ᪨ ᮢ -  ᮡ.
