# hw_01 - Problem Set 1 Fall 09 Due Thursday Sep 17 at 11:00...

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Unformatted text preview: Problem Set 1 Fall 09 Due: Thursday Sep 17 at 11:00 AM in class (i.e., Room 103 Talbot Lab) Please follow the homework format guidelines posted on the class web page: http://www.cs.uiuc.edu/class/fa09/cs373/ 1. DFA/NFA construction. [ Category : Design, Points : 25] (a) For each of the following sets A , construct a DFA or NFA (as indicated) such that its language is A . i. DFA for A = { x ∈ Σ * | for all substring w of x with | w | = 4 , w has at least two 0's } , in which Σ = { , 1 } . ii. NFA for A = { x ∈ Σ * | x contains ab , bc or ca as a substring } , in which Σ = { a,b,c } . iii. DFA for A = { x ∈ Σ * | 111 happens exactly once as a substring in x } , in which Σ = { , 1 } . Note that 1111 / ∈ A . (b) Describe the language accepted by the DFA shown in the gure. q q 2 q 1 q 3 q 5 q 4 1 1 1 1 1 1 2. Set theory. [ Category : Proof, Points : 15] For any two languages A and B prove that ( A * B * ) * = ( A ∪ B ) * ....
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