Module #7: Decidable and Undecidable Problems

Objectives

1. Show there exists a language that is not recursively enumerable
   
2. Define Recursive Language
   
3. Show Halting Problem is undecidable
   
4. Show a language is r.e., but not recursive
   
5. Show the existence of non-r.e.languages
   
6. Reduce Halting Problem to other undecidable problems
   
7. Define the Post Correspondence Problem
   
8. Recognize some undecidable grammar problems
   

Topics

1. Decidability
   
2. Undecidability
   
3. Halting Problem
   
4. Other undecidable Problems
   
5. Post Correspondence Problem
   
6. Undecidable Problems for CFL's
   
7. Reduction
   
8. Closure Properties of CFL's
   

Background Material

0. Texts

Hopcroft, Motwani and Ullman: Chapter 9
Kozen: Lectures 32-35
Sudkamp: 10.4 & Chapter 11

1. Wikepedia: Turing
2. Busch, Shiri & Grahne: Recursively Enumerable and Recursive Languages
3. Busch, Shiri & Grahne: Decidability and an Undecidable Problem: The Halting Problem
4. Busch, Shiri & Grahne: Reducibility and Undecidable Problems
5. Busch, Shiri & Grahne: More Undecidable Problems

Old Homeworks

Homework Fall 05 [PDF]
Solutions [PDF]

Homework Summer 05 [PDF]
Solutions [DOC] [PDF]