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November 8

# November 8 - • If A ≤ T B and B is decidable then A is...

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Do not hand in your homework until the end of class November 8, 2005

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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)

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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-Turing-recognizable, then B  is non-Turing-recognizable
November 8, 2005 Applications of Turing reductions

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Unformatted text preview: • 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-Turing-recognizable, then B is non-Turing-recognizable 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...
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November 8 - • If A ≤ T B and B is decidable then A is...

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