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

Agenda Last week Today Tomorrow Mapping reductions Turing reductions 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-Turing-recognizable, then B is non-Turing-recognizable 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-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 November 8, 2005