048_Computability_theory-part_6

# 048_Computability_theory-part_6 - Selected exercises with...

This preview shows pages 1–3. Sign up to view the full content.

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: Selected exercises with solutions on Computability theory in the field of the Theory of computation Part 6 Amir Semmo Extracted from former homeworks in the course "Theory of computation II", Summer term 2008, University of Potsdam October 6, 2008 Exercise Sheet 6 Exercise 1 Proof by mapping reduction, that the language INFINITE TM = {h M i | M is a Turing Machine and L ( M ) is an in nite language } is undecidable. Specify the reduction and proof that it complies to the de nition of a mapping reduction. We create a mapping function f , which maps A TM on INFINITE TM ( A TM ≤ f INFINITE TM ). If we can nd such a mapping function and assume that INFINITE TM is decid- able, then A TM would be decidable as well, which would be a contradiction. Our function f maps words from A TM on words from INFINITE TM . Let F be the Turing Machine, calculating f : TM F = "On input x : 1. Check if x = h M,w i . If not: Return a description of a Turing Machine N , recognizing the empty language ( L ( N ) = ∅ ) and halt....
View Full Document

## This note was uploaded on 02/22/2010 for the course CS 881 taught by Professor H.f. during the Spring '10 term at Shahid Beheshti University.

### Page1 / 4

048_Computability_theory-part_6 - Selected exercises with...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online