HW6Soln

# HW6Soln - Homework 6 Solution CSCI 2670 3.7 The problem is...

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

Homework 6 Solution CSCI 2670 October 11, 2005 3.7 The problem is with step 2. The Turing machine has to evaluate the polynomial at every possible combination of integer values for x 1 , x 2 , …, x k . Since there are an infinite number of possibilities, the machine will never get past this step and accept if the polynomial has some integer root. 3.15 b) Assume we have two decidable languages A and B. We want to show that A ° B is also decidable. Let M 1 and M 2 be two deciders such that L(M 1 ) = A and L(M 2 ) = B. Consider the following Turing machine: C = “On input w 1 Let l = length(w) 2 For each i = 0, 1, 2, …, l 3 Let w l = the leftmost i symbols in w 4 Let w r = the rightmost l-i symbols in w 5 Run M 1 on input w l 6 If it accepts 7 Run M 2 on input w r 8 If it accepts accept 9 Next i 10 reject Claim: C decides A ° B. This is clear since if w is in A ° B, there is some i for which w l is in A and w r is in B. When the loop reaches that i , C will accept. If w is not in A ° B, then no iteration of the loop will cause C to accept so C will reject as soon as it exits the loop.

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.

{[ 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