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November 1 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing November 1, 2005
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November 1, 2005 Agenda Last week Test & undecidability Today Review one undecidability proof Rice’s Theorem Reductions (Section 5.3)
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November 1, 2005 Announcements Homework due next Tuesday (11/8) 5.7, 5.12 (do not use Rice’s Theorem), 5.20, 5.22, 5.30  b Old text 5.7 Get handout for 5.12, 5.20, 5.22 and 5.30 b Announcements
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November 1, 2005 An undecidable language Let REGULAR TM  = {<M> | M is a  TM and L(M) is a regular language} Theorem :  REGULAR TM  is undecidable Proof :  Assume R decides REGULAR TM  and use R  to decide A TM  (reduce the A TM  problem to the  REGULAR TM  problem). As before, make a new TM, M 2 , that accepts a  regular language iff M accepts w.
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November 1, 2005 Proof (cont.) Consider the following TM S = “On input <M,w> 1. Construct the following TM M 2 M 2  = “On input x 1. If x = 0 n 1 n  for some n,  accept 2. Otherwise, run M on w.  If M accepts w, 
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