048_Computability_theory-part_6

048_Computability_theory-part_6 - Selected exercises with...

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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....
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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.

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048_Computability_theory-part_6 - Selected exercises with...

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