440 CS Test 1
Name: Choose and solve four out of the following six problems. Each problem counts for 3 points. Solving more problems counts for extra credit. 1. Construct DFA's accepting the languages: (i) L consisting of all strings over the alphabet = {0,1} with no consecutive 1's, M = {w {0,1}* | w starts with 10 and ends with 01} , (ii) and then apply the state elimination technique to obtain regular expressions out of them. 2. Let A be a DFA with q0 , q1 , q2 Q , a . Assume that the transition function satisfies conditions: (1) (q0 , a ) = q1 , (2) (q1 , a) = q2 , (3) (q2 , a ) = q0 . ^ Find the formula for (q , a k ) for k = 0,1, 2,3,... and prove it by induction.
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3. (i) (ii) Construct an NFA searching for strings ab, bc, ca (text search for keywords). Assume that the alphabet is = {a, b, c} . Convert NFA your of part (i) to a DFA by the subset construction. Draw a transition diagram of the resulting automaton.
4. Identify languages (i.e. describe them in English) corresponding to the following regular expressions. If there is a restriction on the lengths of strings occurring in the language provide its detailed description. (0 + 10*10*1) * (i) (0 + 2 + 10 + 12)*(1 + ) (ii) a ((a + b + c)(a + b + c)(a + b + c) a) * (iii) 5. Classify the following statements as true or false. Jus...