4.30 Let A be a Turing-recognizable language consisting of descriptions of Turing ma- chines, ((M1), (M2), ...), where every M, is a decider. Prove that some decidable language D is not decided by any decider M, whose description appears in A. (Hint: You may find it helpful to consider an enumerator for A.)

Develop a Turing machine for the language L={w∈{0,1}∗ ||w|isoddandwcontainsatleastone1}. This means that the Turing machine should accept all strings over {0, 1} of odd length that contain at least one 1. Show the state transition diagram in addition to your defi- nition of the Turing machine. Show the working of your Turing machine on the strings “0010”, “00101”, and “000”.

Make a conjecture whether or not it is regular and prove your assertion. When you prove a language is not regular, use the game with demon. Do not apply Pumping Lemma directly.

Make a conjecture whether or not it is regular and prove your assertion. When you prove a language is not regular, use the game with demon. Do not apply Pumping Lemma directly.

Question 7: Prove the non-regularity of the given language L using pumping lemma. L={a"b2na?n}

Could you lend a hand with this issue? I'm struggling with it, and it would be immensely helpful if you could guide me through it, offering detailed explanations at each step to help me grasp the solution better.

Consider the problem of the equivalence of the languages of two DFAs, formulate it as a language, and prove that language is Turing decidable by testing the two DFAs on all strings up to a certain size. Calculate a size will work for it.

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Please solve complete

Present a language B such that B is complete for the class of Turing-decidable languges under ≤m reductions.