Midterm1Solution Finite automata

Midterm1Solution Finite automata - CS 154 Exam 1 Solutions...

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Solutions The test will be open book, open notes, 75 minute time limit. Please write your answers on the exam sheet. Ten problems, 10 points per problem. Unless otherwise specified, the alphabet is {a,b}. 1. Construct a three-state DFA that recognizes the language L whose members contain no aa; that is, every a is either at the end or the beginning or has a b on both sides of it. Exhibit your answer as a transition graph. (For example, L contains the empty string, and the strings ababa, a, abbba, ab, ba, abababa, ababab, but does not contain aa, abaab, or abaa. ) In state q0, we are either at the beginning of the input or have just received a b. In state q1, we have received exactly one a since the last b or the beginning of the input. In state q2, we have received a double a and hence the string will be rejected no matter what we get now or later. 2. Give a regular expression describing the language in problem 1. That is, a regular expression that is matched exactly by strings containing no aa . Answer: b*(abb*)* + b*(abb*)*a. The first term corresponds to strings that are accepted in state q0, the second to strings accepted in state q1. 3.
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Midterm1Solution Finite automata - CS 154 Exam 1 Solutions...

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