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Prove formally that L3 is Turing-recognizable, where L3 = {(M, A) | TM M and DFA A accept a string in common.}
Q1: Which of the following claims are true?* 1 point The recognizable languages are closed under union and intersection The decidable lanquages are closed under union and intersection The class of undecidable languages contains the class of recognizable anguages For every language A, at least one of A or A*c is recognizable Other: This is a required question Q2: Which of the following languages are recognizable? (Select all that apply) 1 point EDFA-{ «A> 1 A is a DFA and...
Please also note that there might be multiple answers for each question. Q1: Which of the following claims are true?* 1 point The recognizable languages are closed under union and intersection The decidable languages are closed under union and intersection The class of undecidable languages contains the class of recognizable languages For every language A, at least one of A or A*c is recognizable Other: This is a required question Q2: Which of the following languages are recognizable? (Select all...
Let n be a positive integer. Classify the languages R = { (M) | M is a TM and L(M) contains exactly n strings} S = { (M) | M is a TM and L(M) contains more than n strings} as (a) decidable (b) Turing-recognizable but not co-Turing recognizable (c) co-Turing recognizable but not Turing-recognizable (d) neither Turing nor co-Turing recognizable
3. (20) Give proofs of the following: a. The question: "Given a DFA M and a string w, does M accept w" is decidable. b. Given two Turing-acceptable language Li and L2, the language LtLz is also Turing-acceptable. [D not use non-determinism. Do be sure to deal with cases where a TM might loop.l
1. Let n be a positive integer. Classify the languages (i) R = {(M)IM is a TM and L(M) contains exactly n strings) (ii) S- (M)|M is a TM and L(M) contains more than n strings as (a) decidable, (b) Turing-recognizable but not co-Turing-recognizable, (c) co-Turing-recognizable but not Turing-recognizable, (d) neither Turing-recognizable nor co-Turing-recognizable. Justify your answers.
obtain a DFA to accept strings of a's and b's starting with the string ab
19. (1 point) Suppose that L is undecidable and L is recognizable. Which of the following could be false? A. I is co-Turing recognizable. B. I is not recognizable. C. I is undecidable. D. L* is not recognizable. E. None of the above. 20. (2 points) Let ETM {(M)|L(M) = 0} and EQTM = {(M1, M2)|L(Mi) = L(M2)}. We want to show that EQTM is undecidable by reducing Etm to EQTM and we do this by assuming R is a...
In class, we talked about how you could encode a DFA as a string, so that a Turing machine could read in that string M, along with another input string w, and determine whether the DFA M accepts w or not. Now, let's think about how we could do this for grammars. In particular, explain how you would encode a grammar as a string g so that a Turing machine could easily take g and an input string w and...
{ <N> : L(M) contains a string starting with a). Rice's theorem can be F 20, L used to prove that LD. T L(M2) >. Rice's theorem can be used to prove T F 21. L that L D. <M,, M2> L(M,) 22. L-( <M,M> : L(M) = L(M2) }, and R is a mapping reduction function from H to L. It is possible that R retur a TM. T F ns <M#>, where M # is the string encoding...