ماشین های تورینگ، تشخیص پذیری و تصمیم پذیری زبان ها

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ماشین های تورینگ, تشخیص پذیری و تصمیم پذیری زبان ها جلسات حل تمرین نظریه زبان ها و ماشین ها دانشگاه صنعتی شریف بهار ۸۷ 

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(Causverciors Gkhow thot o oogquage is decidable PP sowe eoumerdior Pouuverdes the ‏مها‎ ic lexicographic order. ioPicite deviduble fooquage uso subset. 

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طراحی تصمیم گیر ‎x,y,z}‏ 6۰۰۰ رطبع) ی وق بك | وى ‎and s1 and sg are anagrams of each other } ‎ ‎ ‎L={0"1" | mn > 1,n=m?} ‎L= {xyz | € {0,1}4,9 € {0,1} 4} | ‎ ‎PrefixFreepex = {R|R is a regular expression where L(R) is prefix-free} L= {<M >| <M > is an enooding of a DFA and L(M) is finite} ‎INFINITEpra = { (A) : Ais a DFA and L(A) is an infinite language } 

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زبان های مکمل-تشخیص پذیر (عاي‌جوصسوه) EQorg = { (G1,G2) : Gi, Gz are CFGs and L(G1) = L(G2) } 

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زبان های تصمیم پذیر A={(M) : M isa DFA which doesn’t accept any string containing an odd number of Is } L = {(A,R) — DFA A is cqnivalent to the regular expression R} L={(G) : Gis a CEG over {0,1} and 1* L(G) #0} 

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زبان های تصمیم يذير ‎Disa Puig wachiue‏ Oves O toke wore tho k steps oo toput 2? Oves O tuke wore tho k steps vo sow tpt? Oves O take sore thoo A steps ‏مج‎ oll opus? Oves O ever wove the tape head wore thoa A els 

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زبان های تصمیم پذیر 0: 0 the deserts of 0 Parte ‏نا لهس‎ )0( is a Parte ‏مومت‎ L = {(D): DFA D, on some input w, visits each one of its states.} 

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زبان های تصمیم ناپذیر FQere = { (G,H) | G,H are OFGs and L(G) = L(H) }. T ={(M) | M isa TM that accepts w® whenever it accepts w}. = {(M,w)|M on input w ever attempts to move its head left d is on the leftmost tape cell} W Bry = {(M) |M is a 2-tape Turing machine and there exists string w such that M on input w writes L/ on the second tape }, 

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زبان هایْ تشخیص ناپذیر B = {(n,m) | Evory n- state machine M cither halts in less than m steps on an empty input, or docsn’t halt on an empty input}. Let I be a Turing-recognizable language and let: TZ be such that it is 1) not Turing-recognizable. Consider the language: L! = {Ow | € L}U {lw | w ZL}. Is L! Turing-decidable, Turing-recognizable, or not even Turing-recognizable? 

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زبان های تشخیص ‎PLE‏ ‏ترا وه مسا سا و6 L = {<> | Por every put siren wy, D wal alt wahia (DOO |w|° steps } وه مت ‎oot recoenizable, (Reduce‏ سوواط نم توا Let Lz = {(M)|M is a Turing machine and L(M) = ))32(( Prove that Ly is not Turing-recognizable [Just for fun: Is Zo Turing-recognizable?} ‎FEN = {(M)| M accepts only a finite number of strings}‏ و یه 

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طراحی تشخیص دهنده ‎Non — Empty > ]> 2 < | M accepts some string}‏ Let Ly = ((M)|M isa Turing machine and (M) © L(M)} Prove that Ly is Turing-recognizable. A={(Gi,G2) : Gi, G2 are CFGs and L(G1) # L(G2) } 

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‎t7 the Porc dePicitiza bP DOD‏ مسا عووان) ‎Cxenise 9.9: Cena Purtey wacker ever vorite the black syspbol vo its tape? Cun the tape dphobet be the sore us the ‏واه نوت‎ ‏رح( موی‎ wackice's read head ever be to te sae becotiog te ior ‏وه متسه‎ 055 ‏اه ره و اه مه لاس ودف 415 د‎ 

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مت مدا © doubly icPicite tape + festa POs (h>d) * ATuring machine with only RIGHT and RESET moves * Cyclical Turing machine ۰ A queue automaton * 2(k) head Turing machine * Turing machine with k-dimensional tape < A single tape TM not allowed to change the input -> regular language x Only Right and Stay Put moves -> regular language 

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