COMS W3261
Computer Science Theory
Lecture 15: November 12, 2012
The Universal Language and
   Post's Correspondence Problem

Outline

1. The Universal Language is RE but not Recursive

2. Reductions

3. Post's Correspondence Problem

4. Modified PCP

5. Undecidability of the Ambiguity Problem for CFG's

6. Practice Problems

  1. If we can reduce a problem A to a decidable problem B, can we conclude A is decidable?
  2. If we can reduce a decidable problem A to a problem B, can we conclude B is decidable?
  3. If we can reduce a problem A to an undecidable problem B, can we conclude problem A is undecidable?
  4. If we can reduce an undecidable problem A to a problem B, can we conclude problem B is undecidable?
  5. Does the following instance of PCP have a solution: A = (ab, b, aba, aa) and B = (abab, a, b, a)?
  6. Show that the equivalence problem for CFG's is undecidable.

7. Reading Assignment



aho@cs.columbia.edu