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CS311-Automata and Complexity Theory Homework 03 Due Date: Monday, 5th Jan 2004 (at the beginning of class) 1. [20 points] In each of the following, find a simpler regular expression. a. b. c. d. 0*(01)*1* (0*+1*)(0*+1*)(0*+1*) 0*(100*)*1* 1*(0+10)*1* 2. [10 points] Apply theorem 3.4 to obtain a regular expression for the language accepted by the following DFA: a a b b Show all working. 3. [10 points] Find the regular expression corresponding to the following FA, through the state elimination technique. Show all working. 4. [10 points] Construct an NFA, and then a DFA for the language accepting the language L that corresponds to the following regular expression: (11 + 110)0* 5. [10 points] Find the language and the corresponding regular expression of the following FA. Show all working. Start state: Q0 Final State: Q6 The transition table: State Q0 Q1 Q2 Q3 Q4 Q5 Q6 δ(Q,0) Q1 Q3 Q5 Q3 Q5 Q3 Q5 δ(Q,1) Q2 Q4 Q6 Q4 Q6 Q4 Q6 6. [10 points] Give the language and corresponding regular expression for the following FA: 7. [30 points] Draw an FA recognizing the language corresponding to the following regular expressions: a. (0 + 1)*0 b. (11 + 10)* c. (1 + 110)*0 d. (111 + 100)*0 e. 1(01 + 10)* + 0(11 +10)* f. 1(1+10)* +10(0 + 01)*