# hw7 - TM is not Turing-recognizable Problem 4 Let L ={h M...

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

Finite Automata and Theory of Computation October 24, 2006 Handout 15: Homework 7 Professor: Moses Liskov Due: November 2, 2006, in class. Problem 1 Show that L is a Turing-recognizable language if and only if there is a mapping reduction from L to A TM . (This is diﬀerent from showing that there is a mapping reduction from A TM to L , which would prove that L is undecidable.) Problem 2 Show that L is a decidable language if and only if there is a mapping reduction from L to 1 * . Problem 3 Let CF TM = {h M i| M is a TM such that L ( M ) is a context-free language } . (a) Prove CF TM is undecidable. (b) Prove CF
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: TM is not Turing-recognizable. Problem 4 Let L = {h M 1 ,M 2 i| M 1 accepts h M 2 i and M 2 accepts h M 1 i} . (a) Prove that L is Turing-recognizable. (b) Prove that L is undecidable, by giving (and proving) a mapping reduction from A TM to L . Problem 5 Let INF LBA = {h M i| M is an LBA that accepts inﬁnitely many strings } . Prove that INF LBA is undecidable. Problem 6 (optional) Let L = {h M i| M is a TM that includes a state that is never reached on any input } . Prove that L is undecidable. 15-1...
View Full Document

## This note was uploaded on 01/25/2011 for the course CSE 105 taught by Professor Mr.elienasr during the Spring '10 term at American University of Science & Tech.

Ask a homework question - tutors are online