Question

Let FIN = {M L(M) is finite), and recall HP = {M #w | M halts on w). (a) Prove HP <m FIN, where HP is the complement of the halting problem. That is, show there exists a computable function f such that M#w FIN HP iff f(M#we b) Prove HP m FIN. That is, show there exists a computable function f such that (c) Is FIN decidable? Is it recognizable? Justify your answer.

Let F IN = {M | L(M) is finite}, and recall HP = {M#w | M halts on w}.

(a) Prove HP¯ ≤m F IN, where HP¯ is the complement of the halting problem. That is, show there exists a computable function f such that M#w ∈ HP¯ iff f(M#w) ∈ F IN.

(b) Prove HP ≤m F IN. That is, show there exists a computable function f such that M#w ∈ HP iff f(M#w) ∈ F IN.

(c) Is F IN decidable? Is it recognizable? Justify your answer.

Answer 1

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