For a Turing machine M(.) with an input w, let M(w) be the output on the output tape if it stops in finite steps. Let L={(M1, M2, w)| M1 and M2 are Turing machines, w is an input, and M1(w ) is not equal to M2(w)}. Prove that L is undecidable by finding a reduction from Atm to it, where Atm={ |Turing machine M accepts w}.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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For a Turing machine M(.) with an input w, let M(w) be the output on the output tape if it stops in finite steps.  Let L={(M1, M2, w)| M1 and M2 are Turing machines, w is an input, and M1(w ) is not equal to M2(w)}. Prove that L is undecidable by finding a reduction from Atm to it, where Atm={<M,w> |Turing machine M accepts w}.

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