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hw3 - does L M contain a string of the form babb ∪ aa b(b...

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ECS 120: Introduction to Theory of Computation Homework 3 Problem 1. Suppose that L is DFA-acceptable. Show that the following languages are DFA-acceptable, too. Part A. Max ( L ) = { x L : there does not exist a y Σ + for which xy L } . Part B. Echo ( L ) = { a 1 a 1 a 2 a 2 · · · a n a n Σ * : a 1 a 2 · · · a n L } . Problem 2. Prove that the NFA-acceptable languages are closed under reversal. Problem 3. Exhibit decision procedures (algorithms) which answer the following ques- tions. (a) Given a DFA
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Unformatted text preview: , does L ( M ) contain a string of the form ( babb ∪ aa * b ) * ? (b) Given NFAs M 1 and M 2 , is | L ( M 1 ) | = | L ( M 2 ) | < ∞ ? (c) L = {h α i : α is a shortest regular expression whose language is L ( α ) } . Problem 4. Transform the following NFA into a DFA accepting the same language. Bonus (Challenging). If L is a language over the unary alphabet { a } , then L * ∈ Reg . 1...
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