Sofya Raskhodnikova Intro to Theory of Computation L ECTURE 20 Last time Mapping reductions Computation history method Today Computation history method Recursion theorem 3/17/2016 Homework 8 due Practice exam 2 out

I-clicker question (frequency: AC) 3/17/2016 L20.2

I-clicker question (frequency: AC) 3/17/2016 L20.3

I-clicker question (frequency: AC) 3/17/2016 L20.4

Last time We used a computation history method to show that E LBA is undecidable. starting configuration accepting configuration 3/17/2016 L20.5

3/17/2016 Prove that E LBA is undecidable Proof: Suppose to the contrary that TM R decides E LBA. We construct TM S that decides A TM. it rejects L20.6

3/17/2016 ALL PDA is undecidable We can use the computation history method to show that ALL PDA is undecidable. It follows that ALL CFG is undecidable. It follows that EQ CFG is undecidable. L20.7

3/17/2016 A DFA decidable A CFG decidable E DFA decidable E CFG decidable EQ DFA decidable Problems in language theory A TM undecidable E TM undecidable EQ TM undecidable EQ CFG undecidable L20.8

3/17/2016 Post Correspondence Problem L20.9

Recursion Theorem 3/17/2016 Making TMs that can obtain their own descriptions with applications to computer viruses L20.10

3/17/2016 L20.11

S =``Erase input. 1.Run TM A. 2.Run TM B. 3.Halt.’’ 3/17/2016

In English Write this sentence. Write two copies of the following, the second one in quotes: ``Write two copies of the following, the second one in quotes:’’ 3/17/2016 L20.13

Recursion Theorem 3/17/2016 R =``Erase input. 1.Run TM A. 2.Run TM B. 3.Run TM T. 4.Halt.’’ L20.14

Application of recursion theorem 3/17/2016 L20.15