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

2. Agenda Last week Today Tomorrow Mapping reductions Turing reductions
Review
Tomorrow
Begin computational complexity
November 8, 2005

3. Announcement Homework due next Tuesday (11/15)
7.1 (a, b, e, f), 7.2 (a, b, e, f)
November 8, 2005

4. 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

5. 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

6. 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