3. [21 marks] Prove using reductions that the following languages are undecidable. (Do not use Rice's theorem as a black box!) (a) [8 marks] L = {\(M\) | M is a TM and \epsilon \in L(M)}.
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To do this, we can use a reduction from the Halting problem, which is known to be undecidable. The Halting problem is the problem of determining, given a Turing machine M and an input w, whether M halts on w. We will construct a Turing machine R that takes as Show more…
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Question 3-Undecidability: Show, using a reduction from ATM, that the following problem/language is undecidable: Given (encodings of) two Turing Machines M1 and M2 and an input string w, do M1 and M2 have the same output (both accept or both not accept) on input w? That is, prove that the following language is not decidable, by means of a reduction from ATM: E2TM = {<M1, M2, w> | M1 and M2 both accept or both don't accept w}
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