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313F03Malt

313F03Malt - CPSC 313 Alternate Midterm Test Fall 2003 Name...

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CPSC 313 — Alternate Midterm Test Fall, 2003 Name: Lecture Section: Lab Section: Please DO NOT write your ID number on this page. Instructions: Answer all questions in the space provided. No Aids Allowed. This test is out of 50. Duration: 90 minutes

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ID Number: 1. (9 marks) Design a DFA that processes strings over the alphabet Σ = { a, b, c } and that recognizes the intersection, L = L 1 L 2 , of languages L 1 and L 2 , where L 1 = { w Σ * | w includes at least two c ’s } and L 2 = { w Σ * | the length of w is odd } . Give a short explanation, or sketch a short proof, showing that your DFA is correct. Your DFA: Explanation or Proof: 1
ID Number: 2. (8 marks) The following NFA processes strings over the alphabet Σ = { a, b, c } . Con- struct a DFA that is equivalent to this NFA and give a brief justification of your answer. PSfrag replacements Start q 0 q 1 q 2 q 3 a, b, c a b c a Your DFA: Explanation or Proof: 2

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ID Number: 3. Consider the following regular expression, e 1 over the alphabet Σ = { a , b } : ( ab ) * ( bc ) *
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