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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 Turingrecognizable, then A is Turingrecognizable • If A ≤m B and A is nonTuringrecognizable, then B is nonTuringrecognizable
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 Turingrecognizable, then A is Turingrecognizable • If A ≤T B and A is nonTuringrecognizable, then B is nonTuringrecognizable
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.
 Spring '11
 sm

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