University of Nevada Las Vegas
Howard R. Hughes College of Engineering
Department of Computer Science
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CSC 456/656 Assignment 3

Due date: Wednesday, February 13, 2027, 11:30 PM.

All assignments must be handwritten (not typed or printed from a computer file) in your own handwriting, on 8.5 by 11 inch paper, or on A4 paper. Write your name on each sheet, and do not fold the pages or crimp the corners. (You may use a paper clip or a staple.)
Turn the pages in to me or to the graduate assistant on or before the due date.

  1. Recall that LR is the language consisting of the inverses of all strings in a language L.
    Let L be the language over {a,b,c} given by the regular expression (a+b+c)(a+b+c)(b+c)(a+b)*
    1. Draw the state diagram for a DFA M1 with four states (not counting the dead state) which accepts L.
    2. Give a regular expression for LR.
    3. Draw the state diagram for an NFA M2 with four states which accepts LR.
    4. Give the transition function, in tabular form, of a DFA M3 with 16 states (counting the dead state) which accepts LR. (The state diagram of M3 has 16 states and 48 transitions, making it too cumbersome to grade.)
    5. Is M3 a minimal DFA? Explain your answer.
  2. Work Exercise 2.1 on page 154 of the third edition.
    Exercise 2.1 on page 128 of the second edition.
    Exercise 2.1 on page 119 of the first edition.
  3. Work Exercise 2.4 part (e) on page 155 of the third edition.
    Exercise 2.4 part (e) on page 128 of the second edition.
    Exercise 2.4 part (f) on page 120 of the first edition.

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