CMPSCI 401: Theory of Computation

Solutions to First Midterm Exam, Spring 2011

David Mix Barrington

23 February 2011

Directions:

  Q1: 10 points
  Q2: 10 points
  Q3: 10 points
  Q4: 10 points
  Q5: 10 points
  Q6: 10 points
  Q7: 20 points
  Q8: 40 points

  Total: 120 points

Question text is in black, solutions in blue.

Some questions refer to the context-free grammar G which has rules S → aSb, S → bSa, and S → c.

Several questions also refer to the context-free grammar H which has rules S → aS, S → bS, S → Sa, S → Sb, and S → c.

The regular language X is given by the regular expression a*b*.

The regular language Y is given by the regular expression Σ*baΣ*.

Last modified 23 February 2011