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( , , x[1]..x[n] abcd.) . n ( , n-3) , . , , . . x[1]..x[n] , - a. , b, c, , , d. - , abcd . - , . . - , , x : (0), a (1), ab (2), abc (3) abcd (4). , 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 4, . : i:=1; state:=0; {i - , state - } 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); , , abcd . ( , .) , , . - - . , - . , - , . . - , , . . - , , , . ( , - , , , .) (. 1.3) : , - , abcd . , x -> abcd, x 10.2. - . 10.2.1. abcd ? . , , . , , ababc. a, b, a, b. c. - - - , ababc . : c a, : b c, - . , : x y z a b a b a b c .... <- a b a b c <- a b a b c <- , | x y z a b a b | <- | a b a b | c <- | a b | a b c <- | , . - , - . 10.2.2. - ( - ). . - - , . : 0, 1 (a), 2 (ab), 3 (aba), 4 (abab), 5 (ababc). : 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 , , . abab, a, ababa. - (ababc), - aba. : , , , . - , . - . ? . , - - , . , - . , - . : , - . - (. ), , - - . . 10.3. X , - , . ( , , X.) n(X). : n(aba)=a, n(abab)=ab, n(ababa)=aba, n(abc) = - . 10.3.1. , n(X), n(n(X)), n(n(n(X))) .. X. . ( ) - . X. 10.3.2. , ( ). . . . , , X ( X) - n(X), n(n(X)),... . Y X. n(X) - , Y n(X). X, : Y n(X). - , Y n(X). , - , X, , n(X). Y, n(X), n(X), n(n(X)), n(n(n(X))), ..., . 10.4. - - - - () X = x[1]x[2]...x[n] , l[1]..l[n], l[i] = n(x[1]...x[i]) ( n ). : l[i] x[1]..x[i], - . 10.4.1. ? , , A B? . A#B, # - - , A, B. A B , - l , A. 10.4.2. l[1]..l[n]. . , i l[1]..l[i] . (.. x[i+1]) l[i+1]. 1 i i+1 | X | | \Z/ \Z/ , Z x[1]..x[i+1], - - - . ? Z x[i+1]. Z - x[1]..x[i]. , x[1]..x[i], - , x[i+1]. Z. - x[1]..x[i], . - , x[i+1]. . x[i+1], Z. , , , n . : i:=1; l[1]:= 0; { l[1]..l[i] } while i <> n do begin | len := l[i] | {len - x[1]..x[i], | ; | } | while (x[len+1] <> x[i+1]) and (len > 0) do begin | | { , n} | | len := l[len]; | end; | { } | if x[len+1] = x[i+1] do begin | | {x[1]..x[len] - } | | l[i+1] := len+1; | end else begin | | { } | | l[i+1] := 0; | end; | i := i+1; end; 10.4.3. , Cn C. . : . - len 1, l[i+1] l[i]. - , i l[i] 1, - . , l[i+1] <= l[i] - ( i- ) + 1 ( i- ) <= l[i] - l[i+1] + 1 i . 10.4.4. , , X n Y m. ( #, .) C*(n+m), - . , Cn ( - , , , - ). . A#B. - l[1],...,l[n] X m . l[i] i - l[1]..l[n], . X Y , X Y . . 10.4.5. (, - X=x[1]..x[n] Y=y[1]..y[m]). . l[1]..l[n] . : j:=0; len:=0 {len - X, y[1]..j[j]} while (len <> n) and (j <> m) do begin | while (x[len+1] <> y[j+1]) and (len > 0) do begin | | { , n} | | len := l[len]; | end; | { } | if x[len+1] = y[j+1] do begin | | {x[1]..x[len] - } | | len := len+1; | end else begin | | { } | | len := 0; | end; | i := i+1; end; { len=n, X ; Y, X} 10.5. - , - : , . - ? . , , abcd. : , , e, . ( , e , .) , . x[1]..x[n] - , . s - X, k, x[k]=s. pos[s]; - s , pos[s] = 0 ( , ). 10.5.1. pos? . pos[s] 0 for i:=1 to n do begin pos[x[i]]:=i; end; last , . last = m ( ), . last:=m; { } while last <= m do begin { } | if x[m] <> y[last] then begin { } | | last := last + (m - pos[y[last]]); | | {m - pos[y[last]] - , | | y[last] | | . , | | } | end else begin | | , .. | | x[1]..x[m] = y[last-m+1]..y[last], | | ; | | last := last+1; | end; end; , .. ( - ). , - pos[s], m-pos[s], .. - s. . , - last:=last+1 last:=last+(m-u), u - - x[m] . 10.5.2. ? . pos for i:=1 to n-1 do... last:=last+1 last:= last+m-pos[y[last]]; - n ( mn), - - . 10.5.3. , - , mn , . . baaa..aa, a. . ( ) - - , C*(m+n) . , - - . , , . Z (- ) , : Z , . ? , Z, , . . - Z . , ( ) C*(m+n) . 10.6. . , m n. - n . , . . n. - , . - , . ? , - , . - . , . , . , , - . 10.6.1. . . , . - . ( .) , - . - . : . ( , - , , .) 10.6.2. . . p ( , ) x p. - n (- ). - n-1 p x. ( p x , , ). 1 , - x . , . p - , X Y - n. - ( , - p, - ). , x , 0. n-1 n-1 - . , n p, x . 10.7. , . , a?b, ? ( , b 2 a). 10.7.1 , , a?b. . , , a - . : 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 - (*), . , - ab*cd , ab, - , ( ) cd. 10.7.2. , , ab*cd ( ). . 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 - . 10.7.3. X[1],...,X[k] Y. - , X[i] Y ( - ). , - ( , ). . , ( ). (- k Y). . - . , - . - . ( ) . - ( ) . - - . , , , . , . : - ( , ). , - . , {aaa, aab, abab} a/ * a a / b * * * * \b a b \ * * * , - , . , : - - ( ) , - (= , - ). n, . , n(P) = , - P. (, - .) - : 10.7.4. P - . , , P, {n(P), n(n(P)),...} . . - - . , , P y . - P, n(P), n(n(P)) .., , - y. , , . , n . , n n. , . , ( - ). . . , - . , , - . . , - l, e, (, ), * | ( - - ). : () - ; () l, e - ; () A,B,C,..,E - , (ABC...E) - . () A,B,C,..,E - , (A|B|C|...|E) - . () A - , A* - - . : () , , ; () e , l - , ; () (ABC...E) , , A B, C,..., E (- ); () (A|B|C|...|E) , A,B,C,..,E; () A* - , A, , , , A. ( , - A*.) (a|b)* a b (aa)* a (l|a|b|aa|ab|ba|bb) 2 a,b 10.7.5. , - a b, a . . b* a, (b* a b* a b*) - a. , : ((b* a b* a b*) | b*)* 10.7.6. , - a,b,c, bac . . ((a|b|c)* bac (a|b|c)*) - : , , - . 10.7.7. a?b ab*cd, ? ( * - , !) , - a,b,c,d,e. . ((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. , , - . . - ( ). - () , (). - ( ). - - . . , ( , ). , , . - , . . , - , , - . . , - . , , . 10.7.9. , - . . . - . - : || >|*1 1*|->- / || \ / || \ * >|*2 2*|>* \ || / \ || / >|*3 3*|> || , - - , ; . ( 6) . || || || *>|*1 1*|>|*2 2*| >|*3 3*|>* || || || , *>*>* / \ / \ | | V ^ | | - | *1 1* | - 10.7.10. . , - , , (.. , ). . - . , X , , , X. , , . , : 10.7.11. . , - , . . ( .) 1..k. , 1 - , k - . D[i,j, s] , i j, 1,...,s. , D[1,k,k]. s D[i,j,s] i j. s=0 ( , ). D[i,j,s+1]? - , s+1- . - , . - , 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])) ( : ). - . 10.7.12. ? . , . 9 ( ). 10.7.13. , , - , , - , ( - , - - ). . . . . , , - . - .  6' /@F e PGMMd!(xKddd0dPC ..RTF@ !$%%% /00*@7*((.@8.1x1@x/x/| | } @} } ~ ~ @     @    @     @     @   @  @     @    @     @     @   @  @     @    @     @     @   @  @     @    @  Root Entry 9\PageMaker8cg)  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~PageMaker 5.0 RGB DAdobe Compatibility CMS Adobe Compatibility CMSPageMaker 5.0 CMYKNTHarmonicaNTTierceParsek"PeterburgPragmaboldPragmaticaCTTSchoolBookSigns"TextBook"Time RomanTimes NR Cyr MTUkrainianTextBook"UkrainianTimesETUnivers Condensed Cyr"Univers Cyr"Xenia"XeniaCondensed"XeniaExtended"Baskerville Win95BTZurich Win95BT"Academy HoAcademy ItalicAdverGothic 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