CS 390 Test I
February 20, 1996
1. Which of the following statements are true and which are false ?
(a) If , then .
(b) The function defined as is one-to-one.
(c) Let A be the domain of a function f, let and let .
Then .
(d) If languages and are regular, then is regular.
(e)

2. Find a regular expression for the languages of strings over the alphabet {0,1} containing exactly three 0's.

3. Consider the language of strings consisting of one or more a's followed by zero or more b's. The alphabet for this language is .
(a) What is the shortest string of this language ?
(b) List all the strings of length 2 of this language.
(c) List all the strings of length 3 of this language.
(d) Show how strings of length 2 are generated from strings of length 1.
(e) Show how strings of length 3 are generated from strings of length 2.
(f) Inductively define this language.

4. Prove by induction that a language consisting of a single string is regular.

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