The notion of a verifier is central to the definition of the complexity class NP. However, we can consider the idea of a verifier independent of ideas from complexity theory. Recall that a verifier for a language L is an TM V such that L = {w | V accepts for some c}
1. The notion of a verifier is central to the definition of the complexity class NP. However, we can consider the idea of a verifier independent of ideas from complexity theory. Recall that a verifier for a language L is an TM V such that
L = {w | V accepts <w, c> for some c}.
Prove that ATM, the acceptance language for Turing machines, has a verifier even if we add the extra condition that the verifier is a decider. Note that the verifier need not run in polynomial time. We are not asking for a polynomial-time verifier.
2. Let L be a context-free language. Prove that L is NP-Complete if and only if P = NP.
3. For a string w, let w_rev be the string w reversed.
For any language A, Let reverse(A) = { w_rev| w is in A}.
For which of the following classes of languages is closed under the reverse operation. In other words, for which classes is it true that for every language A in the class, reverse(A) is also in the class.
Context-Free languages(Closed or Not Closed)
Nonregular languages(Closed or Not Closed)
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