{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Quiz7Soln

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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern