November 8

November 8 - Do not hand in your homework until the end of...

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Unformatted text preview: Do not hand in your homework until the end of class November 8, 2005 Agenda • Last week – Mapping reductions – Turing reductions • Today – Review • Tomorrow – Begin computational complexity November 8, 2005 Announcement • Homework due next Tuesday (11/15) – 7.1 (a, b, e, f), 7.2 (a, b, e, f) November 8, 2005 Applications of mapping reductions • If A ≤m B and B is decidable, then A is decidable • If A ≤m B and A is undecidable, then B is undecidable • If A ≤m B and B is Turing-recognizable, then A is Turing-recognizable • If A ≤m B and A is non-Turingrecognizable, then B is non-Turingrecognizable November 8, 2005 Applications of Turing reductions • If A ≤T B and B is decidable, then A is decidable • If A ≤T B and A is undecidable, then B is undecidable • If A ≤T B and B is Turing-recognizable, then A is Turing-recognizable • If A ≤T B and A is non-Turingrecognizable, then B is non-Turingrecognizable November 8, 2005 Today we will do examples • Hint for problem 5.20 • Show that L1 = {<M> | M is a TM and M halts on at least one input} is undecidable • Is L2 = {<M,w,t> | M is a TM that accepts w in at least t steps} decidable? Prove your answer • From Sipser – 5.13, 5.14, 5.15, 5.24, 5.30 c November 8, 2005 ...
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This note was uploaded on 02/07/2011 for the course CS 501 taught by Professor Sm during the Spring '11 term at Indiana.

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