355mt1solf10 - CSE 355 Fall 2010 Colbourn Theory of...

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CSE 355 Theory of Computing ID: ___________ Fall 2010 - Colbourn Midterm # 1 Page 1 of 6 30 September 2010 NAME Ima Sample ASU ID 0123456789 You have one hour and 15 minutes to complete the exam. Do not open the exam until instructed to do so. No notes, texts, computers, calculators, or communication devices are permitted. Write all answers on the examination paper itself. BUDGET YOUR TIME WELL! SHOW ALL WORK! Question 1 [15] Question 2 [10] Question 3 [8] Question 4 [12] Question 5 [5] Total [50] Bonus question [1 mark]: What is the language *? It is { λ }. Grades out of 50 are: 10 11 11 12 14 15 16 16 17 18 19 20 22 23 23 25 25 25 26 26 27 27 29 30 31 32 34 35 36 36 36 37 37 38 40 43 43 44 44
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CSE 355 Theory of Computing ID: ___________ Fall 2010 - Colbourn Midterm # 1 Page 2 of 6 Question 1. [15 marks total] Consider the language L over {a,b} in which every b is immediately preceded by at least two consecutive a’s. (a) [5 marks] Give an NFA- λ for L. (Q, Σ , δ ,q0,F) with Q ={q0,q1,q2}; Σ = {a,b}, F = {q0,q1,q2}, and δ defined by δ (q0,a) = {q0,q1}, δ (q1,a) = {q2}, and δ (q2,b) = {q0} (b) [5 marks] Using the algorithm developed in class, from the NFA- λ , form a regular expression for L. (Describe briefly the steps that you follow.) I make the machine above have only one accept state by adding a new state q3 with transitions δ (q0, λ ) = {q3}, δ (q1, λ ) = {q3}, δ (q2, λ ) = {q3}, and then change the accepting states to F = {q3}. Then I use the algorithm from class to remove states q1 and q2 to get (a aab)* (c) [5 marks] Using the algorithm developed in class, convert this NFA- λ to a DFA.
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