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The language of the DFA M in Example 6.3.4 consists of all strings over $\{a, b\}$ with an even number of $a$ 's and an odd number of $b$ 's. Use Algorithm 7.2.2 to construct a regular expression for $L(M)$. Exercise 2.37 requested a nonalgorithmic construction of a regular expression for this language, which, as you now see, is a formidable task.

   The language of the DFA M in Example 6.3.4 consists of all strings over $\{a, b\}$ with an even number of $a$ 's and an odd number of $b$ 's. Use Algorithm 7.2.2 to construct a regular expression for $L(M)$. Exercise 2.37 requested a nonalgorithmic construction of a regular expression for this language, which, as you now see, is a formidable task.

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Languages and Machines: An Introduction to the Theory of Computer Science

Languages and Machines: An Introduction to the Theory of Computer Science

Thomas A. Sudkamp 2nd Edition

Chapter 7, Problem 3

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Step 1

Let's define the states: - \(q_0\): even number of \(a\)'s, odd number of \(b\)'s (initial and accepting state) - \(q_1\): odd number of \(a\)'s, odd number of \(b\)'s - \(q_2\): even number of \(a\)'s, even number of \(b\)'s - \(q_3\): odd number of \(a\)'s, even Show more…

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The language of the DFA M in Example 6.3.4 consists of all strings over $\{a, b\}$ with an even number of $a$ 's and an odd number of $b$ 's. Use Algorithm 7.2.2 to construct a regular expression for $L(M)$. Exercise 2.37 requested a nonalgorithmic construction of a regular expression for this language, which, as you now see, is a formidable task.

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