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Unformatted text preview: Homework 2 CISC 303 Timo Kötzing ([email protected]) Handed out: Monday, February 16. Due Date: Friday, February 27. Note that the Problem 1 gives you a choice of two parts, you don't need to submit both (no extra credit for submitting both parts). Further note that the last problem is an extra credit problem. Problem 1. (8 points) Do EITHER ONE of (A) or (B) below. You do not need to hand in solutions to both problems . (A) Let S be a set, let M,N ⊆ S . For each T ⊆ S , we write T for S \ T (all elements of S that are not in T ). Prove, in detail, the following set-theoretic claims. (i) M = M ; (ii) M ∪ N = M ∩ N ; (iii) M ∩ N = M ∪ N ; (iv) M \ N = M ∩ N ; (v) M = N ⇔ ( M \ N ) ∪ ( N \ M ) = ∅ . (B) Let M = ( A,Q,δ,F,q ) be a DFA. Let v,w ∈ A * be such that δ * ( q ,v ) = δ * ( q ,w ) . (1) Use Equation (1) to show ∀ u ∈ A * : δ * ( q ,vu ) = δ * ( q ,wu ) . (2) Then conclude ∀ u ∈ A * : vu ∈ L ( M ) ⇔ wu ∈ L ( M ) . (3) Hint: Prove (2) by induction: rst show it is true for u = ε ; then suppose it is true for some...
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This note was uploaded on 02/01/2012 for the course CISC 303 taught by Professor Carberry,m during the Spring '08 term at University of Delaware.
- Spring '08