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
6. Video of Decidability
7. Video of Halting Problem
8. Video of A language that is not re and Intro to reducibility
9. Video of More undecidable via reducibility
10. Video of Rice's Theorem

Old Homeworks

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