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Quiz7Soln - I have written the first line of P for you P =...

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CSCI 2670 Intro. to Theory of Comp. Quiz 8 11/3/05 Name: ________________________________ In this quiz, you will prove the following language is undecidable FINITE TM = {<M> | M is a TM and L(M) is finite}. The quiz has 4 questions. If you skip a question, you can answer the next question as though you had answered the previous one. For example, in (2) you are asked to create a Turing machine P and in (3) you need to use P. You can use P in (3) even if you couldn’t successfully create P in (2). Assume FINITE TM is decidable and that F decides it. (1) (1 point) Pick any finite language, call it FL. FL = {0,00,000} (2) (3 points) Create a Turing machine P satisfying the following property: L(P) = Σ* If M accepts w L(P) = FL Otherwise You do not need to argue that this property is satisfied.
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Unformatted text preview: I have written the first line of P for you. P = “On input x: 1. If x ∈ FL, accept 2. Run M on input w 3. If M accepts w, accept ” (3) (3 points) Using F (the decider for FINITE TM ) and P (your answer to (2)), create a decider S for A TM . You don’t need to argue that S is a decider or that L(S)=A TM . S = “On input <M,w>, where M is a TM 1. Create TM P from question (2) 2. Submit <P> to TM F 3. If F accepts <P>, reject 4. If F rejects <P>, accept ” (4) (3 point) Based on the decider presented in (3), what can you conclude? Why does your conclusion follow? FINITE TM is not decidable. This follows because (3) demonstrates that if FINITE TM is decidable, then A TM is also decidable, but we know that A TM is undecidable....
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