CMPSCI 401: Theory of Computation

Solutions to Second Midterm Exam, Spring 2010

David Mix Barrington

2 April 2010

Directions:

  Q1: 10 points
  Q2: 10 points
  Q3: 10 points
  Q4: 10 points
  Q5: 35 points
  Q6: 30 points
  Q7: 20 points

  Total: 125 points

If X is a computational model, such as DFA's, CFG's, or TM's, we follow Sipser in defining the following languages:

Recall also that the Post Correspondence Problem takes as input a finite set of dominoes {D1,..., Dn}, such that each domino Di has a top string ti and a bottom string bi, each a nonempty string in &Sigma'* for some alphabet Σ. A set of dominoes is in the language PCP if there exists a nonempty sequence of dominoes that is a match, meaning that the concatenation of the top strings and the concatenation of the bottom strings form the same word.

Last modified 2 April 2010