# hw11 - Computer Science 340 Reasoning about Computation...

• Homework Help
• PresidentHackerCaribou10582
• 1

This preview shows page 1. Sign up to view the full content.

Computer Science 340 Reasoning about Computation Homework 11 Due on Friday, December 14, 2007 For this homework, read Section 5.3 on Mapping Reducibility in the notes distributed in class. Problem 1 Recall that E TM = { M | M is a TM and L ( M ) = ∅} . Prove that E TM is Turing-recognizable. Problem 2 Suppose that language A is mapping reducible to language B . (See definition 5.15 for an explanation of what this means.) Show that if A is not Turing-recognizable then B is not Turing-recognizable. Conclude that there is no mapping reduction from A TM to E TM . Recall that A TM = { M, w | M is a TM and M accepts on input w } . Problem 3 Let J = { w | w = 0 x for some x A
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A TM or w = 1 y for some y ∈ A TM } . In other words, J is the union of all strings in A TM with a 0 appended in front of them, and all strings in A TM with a 1 appended in front of them. Show that neither J nor J is Turing-recognizable. Problem 4 Show that the Post Correspondence Problem (PCP) over a binary alphabet (i.e. over the alphabet Σ = { , 1 } ) is undecidable. Hint: Give a reduction from PCP over an arbitrary alphabet to PCP over a binary alphabet. You may use the fact that PCP over an arbitrary alphabet is undecidable....
View Full Document

• Fall '07
• CharikarandChazelle
• Computer Science, Logic, Computational complexity theory, Turing reduction, Many-one reduction, Log-space reduction

{[ 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