COMS W3261 CS Theory
Lecture 18: Undecidable Problems

1. PCP and Modified PCP are Undecidable

2. Undecidable Problems about Turing Machines

3. Undecidable Problems about Context-free Languages

4. Practice Problems

  1. Show that if the complement of a language L is undecidable, then L itself is undecidable.
  2. Show that the Halting Problem is recursively enumerable but not recursive.
  3. Show that it is undecidable whether the language accepted by a TM is infinite.
  4. Show that the complement of the list language LA [HMU, p. 413] is context free.
  5. Show that it is undecidable whether the language generated by one context-free grammar is contained within the language generated by another context-free grammar.
  6. Let L be the set of CFG’s G such that L(G) contains at least one palindrome. Show that L is undecidable.
  7. Give an example of a language L such that both L and the complement of L are not recursively enumerable.

5. Reading Assignment