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Let $\mathrm{G}$ be the grammar $$ \text { G: } \begin{aligned} S & \rightarrow a S|b A| a \\ A & \rightarrow a S|b A| b . \end{aligned} $$ a) Use Theorem 7.3.1 to build an NFA M that accepts L(G). b) Using the result of part (a), build a DFA M' that accepts L(G). c) Construct a regular grammar from $M$ that generates $L(M)$. d) Construct a regular grammar from $M^{\prime}$ that generates $L\left(M^{\prime}\right)$. e) Give a regular expression for $L(G)$.

   Let $\mathrm{G}$ be the grammar
$$
\text { G: } \begin{aligned}
S & \rightarrow a S|b A| a \\
A & \rightarrow a S|b A| b .
\end{aligned}
$$
a) Use Theorem 7.3.1 to build an NFA M that accepts L(G).
b) Using the result of part (a), build a DFA M' that accepts L(G).
c) Construct a regular grammar from $M$ that generates $L(M)$.
d) Construct a regular grammar from $M^{\prime}$ that generates $L\left(M^{\prime}\right)$.
e) Give a regular expression for $L(G)$.

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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 4

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Step 1

3.1** Theorem 7.3.1 states that for each nonterminal in a grammar, we can create a state in the NFA, and for each production, we create a transition. The initial state of the NFA is the start symbol of the grammar. - States: $\{S, A\}$ - Alphabet: $\{a, b\}$ - Show more…

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Let $\mathrm{G}$ be the grammar $$ \text { G: } \begin{aligned} S & \rightarrow a S|b A| a \\ A & \rightarrow a S|b A| b . \end{aligned} $$ a) Use Theorem 7.3.1 to build an NFA M that accepts L(G). b) Using the result of part (a), build a DFA M' that accepts L(G). c) Construct a regular grammar from $M$ that generates $L(M)$. d) Construct a regular grammar from $M^{\prime}$ that generates $L\left(M^{\prime}\right)$. e) Give a regular expression for $L(G)$.

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