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16 a a,b _ b 1 2 b I+0.2. W68 '&0*1 (/#*1.+%.1'&<*&M#CM+A 31)13 JF 3#00?&"31.+% 3+0(.,&- 0*1/(1", D"& - '13-&? 0&0"&%.++.# -A&/.1 /&*21. '&/#-#"$0% 0+?-&* b, +.#D1 L"& '3+-1/1", F#@+,*+-#.+C.!&&"-1"0"-1..&, '13-=; 0+?-&* /&*21. )="$ a. GD+"=-#%, D"& "13?+.#*$.&1 0&0"&%.+1 &/.& -"&3&1,?&2.& ("-132/#"$, D"& #-"&?#" /&'(0,#1" /-1 0"3&,+: aaa + abb. W1;0"-+"1*$.&, &"-1" /-#. a '=5"'#%&# ':<#? =.#)- "#$#%&8 I#00?#"3+-#1?#% F#/#D# /&0"#"&D.& 0"#./#3".#, :1.+1 A&3&:& '&//#1"0% 0&)+3#.+C +F «,+3'+D+,&-»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«,+3'+D+,&?». 53#,"+D10,&1 0&&)3#21.+1: #*>#-+"?&21" 0&0"&%"$ +F 26 0+?-&*&- ( A = 26).!"3&,#?&21" )="$ +F 60 0+?-&*&-. 4#*& L"&<&, &)M11 '31/0"#-*1.+1 &,&.1D.=A #-"&?#"#A 0-+/1"1*$0"-(1" & "&?, D"& -01 0"3&,+?&<(" /&'(0,#"$0%. V&</# &"-1" )(/1" 26 60, D"& -10$?#?.&<&. P#0,&*$,&?.&<&? 53+.#*+D++,&?'$C"13# +*+ A&3&:1<&,#*$,(*%"&3#,.# L"&" -&'3&0 &"-1"+"$ *1<,&. 9'31/1*+? log 10 (26 60 ) = 60log 10 (26) = 60(ln(26) / ln(10))! 60 * 1.415! 84.9.!*1/&-#"1*$.&, - &"-1"1?&21" )="$ - /10%"+D.&? '31/0"#-*1.++. V#,&1,&*+D10"-& 0"3&,.1 '&?10"+"0% - 0"#./#3".=; "+' (-+/# Integer). 5&L"&?( '3+.#'+0#.++ 31:1.+%.# %F=,1 Pascal '3+/1"0% -3(D.(C 31#*+F&-#"$ #3+>?1"+,( '&-=:1..&; "&D.&0"+.!&&"-1"0"-(CM+1 >(.,@++ "#,21 &".&0%"0%, 3#F3%/( «,+3'+D+,&-», -A&/%M+A - &)%F#"1*$.(C '&/<&"&-,(. 16

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state, k) "1,(M11 0&0"&%.+1 state, + '3&:*& k :#<&-. I#00?&"3+? 0"3&,+ /*+.= k, &)*#/#CM+1 0*1/(CM+? 0-&;0"-&?: '&*(D+-.# -A&/ "#,(C 0"3&,(, W68 '3+A&/+" +F.#D#*$.&<& 0&0"&%.+% - 0&0"&%.+1 state. 9)&F.#D+? D+0*& L"+A 0"3&, D131F f(state, k). H=D+0*1.+1 L"&<& F.#D1.+% /*% 3#F*+D.=A '#3 (state, k) + %-*%1"0% '&/F#/#D1;. W*% (0'1:.&<& '3+?1.1.+% /+.#?+D10,&<& '3&<3#??+3&-#.+%.1&)A&/+?= 31,(331.".=1 0&&".&:1.+%,,&"&3=1 *1<,& '&*(D#C"0%, (D+"=-#% ('&?%.("=1 0-&;0"-#,&.1D.&<& #-"&?#"# /1? L"+ 0&&".&:1.+%: # 1, state = initial f ( state,0) = "! 0, state $ initial f ( state, k) = f ( st, k # 1)! st" U, c" A $ ( st, c) = state </1 initial.#d#*$.&1 0&0"&%.+1 W68.!>&3?(*+3(1? 0A1?( 31:1.+%, 0&0"&%M1<& +F /-(A L"#'& #M#1? W68 0.1'&<*&M#CM+?+ 31)3#?+ - W68 )1F "#,&-=A. P#*+D+1 31:1.+% 0 '&?&M$C /+.#?+D10,&<& '3&<3#??+3&-#.+% /*% W68 )1F.1'&<*&M#CM+A 31)13 (,31'*%1" (-131..&0"$ - "&?, D"& L>>1,"+-.&1 (0"3# '&<*&M#CM+A 31)13 "#,21 -&F?&2.& ?1.%1? /+.#?+D10,&1 '3&<3#??+3&-#.+1, +0'&*$F(% -=:1'3+-1/1..&1 31,(331.".&1 0&&".&:1.+1. N1*10&&)3#F.&, A&"% +.1 &)%F#"1*$.&, +0'&*$F&-#"$ /+.#?+D10,&1 '3&<3#??+3&-#.+1 «0.+F( --13A». W*%.#A&2/1.+% &"-1"#.1&)A&/+?& )(/1" '3&0(??+3&-#"$! t"t f ( t, n) f(terminal_state, n) '& -01? "13?+.#*$.=? 0&0"&%.+%? t. H F#,*CD1.+1 3#F/1*# &"?1"+?, D"& '3+? /+.#?+D10,&<& '3&<3#??+3&-#.+%.#,&.1D.&? #-"&?#"1,,#, + -&&)M1.# <3#>1, %-*%1"0% &D1.$ L>>1,"+-.=?. 5131,3=-#CM+10% '&/F#/#D+ #-"&?#"+D10,+ -=/1*%C"0%:.1&)A&/+?& *+:$ >(.,@+C -& -01A 0&0"&%.+%A #-"&?#"#. H,#D10"-1 '3+?13#?&2.& '3+-10"+ F#/#D(, '3+ 31:1.++,&"&3&; +0'&*$F(1"0%, 17

18 "1A.+,#, '&*.&0"$C #.#*&<+D.#% -"&3&; D#0"+ 31:1.+%.#0"&%M1; F#/#D+: F#/#D# «Currency Exchange» («9)?1. -#*C"=»). 8-"&3: P+,&*#; W(3&-. J0"&D.+,: B1"-13"$>+.#* NEERC-2001, =; '&/31<+&.. O#/#D# 3#F?1M1.#.# 0#;"1 '&/.&?13&? Z#,"+D10,+?#"1?#"+D10,#%?&/1*$ L"&; F#/#D+ %-*%1"0%,&.1D.=? #-"&?#"&?, </1 0&0"&%.+%?+ %-*%C"0% -#*C"=, # '131A&/#?+?12/(.+?+ &)?1..=1 '(.,"=.!*1/(1" (,#F#"$ 1M1 &/.( +F-10".(C F#/#D(: «Censored!» («N1.F(3#!»). 8-"&3: P+,&*#; W(3&-. J0"&D.+,: B1"-13"$>+.#* NEERC-2001, =; '&/31<+&.. O#/#D# 3#F?1M1.#.# 0#;"1 '&/.&?13&? I#0'3&0"3#.1..=; 0'&0&) 11 31:1.+% 0&0"&+" +F /-(A L"#'&-: '&0"3&1.+1,&.1D.&<& #-"&?#"#, 3#0'&F.#CM1<&.#)&3 0"3&, (#*<&3+"? '&0"3&1.+%.#F=-#C" #*<&3+"?&? 8A&-6&3#0+,#), + +0'&*$F&-#.+1 /+.#?+D10,&<& '3&<3#??+3&-#.+%.# '&*(D1..&?,&.1D.&? #-"&?#"1. 5&A&2#% F#/#D# )1F /+.#?+D10,&<& '3&<3#??+3&-#.+% F#/#D# «Obscene words filter» («Z+*$"3 <3()=A 0*&-»). 8-"&3: 5#-1* 8".#:1-. J0"&D.+,: D1?'+&.#" G3UG O#/#D# 3#F?1M1.#.# 0#;"1 '&/.&?13&? &C )=*+ '3&#.#*+F+3&-#.= -01 F#/#D+ - #3A+-#A &*+?'+#/.=A F#/#D '13-&1 +C.% 2005 <&/#. 63&?1 F#/#D+, 3#00?#"3+-#1?&; -.#0"&%M1; 0"#"$1, + "31A "&*$,& D"& ('&?%.("=A F#/#D, - &0"#*$.=A F#/#D#A +0'&*$F&-#.+1,&.1D.=A #-"&?#"&- &<3#.+D+-#1"0% #*<&3+"?&? 6.("#-4&33+0#-53#""# '29+ I#00?&"3+? '13-=; L"#'. 6#, 1<& -='&*.+"$? H 3#F/. 3.2 («5&0"3&1.+1?#"1?#"+D10,&;?&/1*+»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«P1/&'(0,»,,&"&3&1.1 %-*%1"0% "13?+.#*$.=?. 9.& F#?,.("&.# 01)% '3+ '131A&/1 '& -01? 0+?-&*#?. 5&'#/#.+1 - L"& 0&0"&%.+1 )(/1" 0&&"-1"0"-&-#"$ -A&/( +F.1'&<*&M#CM+A 31) A&/.&? #-"&?#"1. P1'&031/0"-1..&1 «'3&<&-#3+-#.+1» 31:1.+% '3+-1*&,.1'*&A&?( 31F(*$"#"(. 9@1.+? L>>1,"+-.&0"$ 31:1.+%. 6#, &'31/1*+"$, D"& '3&+F&:*& '&'#/#.+1 K0*+ F# U :#<&- #-"&?#".1 '131;/1" '&.1'&<*&M#CM1?( 31)3(, "& L"& )(/1" &F.#D#"$, D"& &. -&:1* ( U D+0*& 0&0"&%.+; #-"&?#"#). H13A.%% &@1.,# -31?1.+ 3#)&"=: U * U * A '&3%/,# 26 *

19 4.&<& L"& +*+?#*&? 5&?13,#? 2003 <&/#, -,&"&3&? )=*# '31/*&21.# F#/#D#, F# 01,(./(?&2.& )=*& -='&*.+"$ &-01? '3&0"=A &'13#@+;.# %F=,1 -=0&,&<& (3&-.%, "#,&?,,#, %F=,+ Pascal +*+ C++.!&&"-1"0"-1..&, "#,&; 0'&0&) (0"3#.1.+%.1'&<*&M#CM+A 31)13 /&*21. "31)&-#"$.1 )&*11 01,(./=, D"& - '13-&? '3+)* '31/0"#-*%1"0% /&'(0"+?=? &/+. +F /-(A L"#'&- "31)(1" '&*&-+.( -31?1.+, -1/$ &<3#.+D1.+1.# &/+. "10" 0&0"#-*%1" /-1 01,(./=,,#, 0,#F#.& - (0*& /1? '01-/&,&/ /*% (0"3#.1.+%.1'&<*&M#CM+A 31)13. H '01-/&,&/1?.&210"-& -01A 0&0"&%.+; &)&F.#D1.& D131F State. for c in Alpha do // (/ -4,+ 4*+-/ *73 for i in State do // (/ -4,+ 4/47/81*8+ 3-7/+373 cur := i // 9,:;<,, 4/47/81*, z := n // =/5*>,47-/ 4/47/81*? // (/:3 ),@)/-A,),./0 *B 4/47/81*8 k A/ 4*+-/5; j // A/C5/<3D<,,, *,<, 40,531/ 1, />,1E +1/C/ A,),./0/- while ("[cur,c] = 1) and (z > 0) do cur := #[cur][c] // (,),?7* z := z 1 // F+,1EG*7E 4>,7>*: end // H45* -4,,<, />,),01/, ),@)/ 1,A/C5/<3D<,, if ("[cur][c] = 1) then #[i][c] := 0 // I13>*7 J*:5 else #[i][c] := #[cur][c] // K13>, A,),473-58,+ ),@)/ // K 7,A,)E 41*+3,+ A/+,7:; «1,A/C5/<3D<,, ),@)/» "[i][j] := 0 end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«0.+F( --13A» /*% '&+0,# &"-1"#. H 0&&"-1"0"-++ 0 "1&3+1;, -=3#2#1? &"-1" '&/F#/#D+ D131F &"-1"=, 3#.11.#;/1..=1 /*% /3(<+A '&/F#/#D. E"& &0(M10"-*%1"0% 0*1/(CM+? &)3#F&?. I1,(331.".=1 0&&".&:1.+%, '3+-1/1..=1-3#F/. 3.3, -=3#2#C" F.#D1.+1 >(.,@++ f(state, k) D131F F.#D1.+% >(.,@++ f(st, k-1) /*% 3#F*+D.=A 0&0"&%.+; st $ U. 9/.#,& /*% /#..&<& 0&0"&%.+% state.1(/&).& &'31/1*%"$, +F,#,&<& 0&0"&%.+% st?&< '3&+F&;"+ '131A&/ - L"& 0&0"&%.+1.# '31/=/(M1? :#<1. 5&L"&?( (/&).11 F#>+,0+3&-#"$ '#3( (state, k) +, '131)+3#% ?-&*= 19