60 PS8 Solutions

# 60 PS8 Solutions - Handout#60 June 2 2010 CS103 Robert...

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Handout #60 CS103 June 2, 2010 Robert Plummer Problem Set #8 Solutions All problems are from Sipser. 1. Exercise 4.2, p. 183. EQ DFA,REX = { A, R | A a DFA, R a regular expression and L(A) = L(R)} The following TM E decides EQ DFA,REX : E = "On input A, R : 1. Convert regular expression R to an equivalent DFA B using the procedure given in Theorem 1.54. 2. Use the TM F for deciding EQ DFA given in Theorem 4.5 on input A, B . 3. If F accepts, accept . If F rejects, reject ." 2. Problem 4.12, p. 183. Note that L(R) L(S) if and only if L(S) L(R) = . The following TM decides A: X = "On input R, S where R and S are regular expressions: 1. Construct DFA E such that L(E) = L(S) L(R). 2. Run TM T for deciding E DFA from Theorem 4.4 on E . 3. If T accepts, accept . If T rejects, reject ." 3. Problem 4.15, p. 184. The following TM X decides A: X = "On input R where R is a regular expression: 1. Construct DFA E that accepts *111 *. 2. Construct DFA B such that L(B) = L(R)

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60 PS8 Solutions - Handout#60 June 2 2010 CS103 Robert...

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