Chapter 2, Problem 9E

Explanation of Solution

a.

Description of the given regular expression:

The given regular expression is a* (b a* b a*)*.

• Here, “a” and “b” are the terminal symbols and t...

Explanation of Solution

b.

Unambiguous context-free grammar:

Unambiguous context-free grammar for the given regular expression is as follows:

$\begin{array}{l}\text{G }\to \text{ As S}\\ \text{S}\to \end{array}$

Explanation of Solution

c.

Canonical (right-most) derivation of the given string:

• Canonical derivation is a leftmost or rightmost derivations that may not be unique but they allow describing a derivation by the sequence of production rules taken.
• In the rightmost derivation, the rightmost nonterminal on the right hand side of a rule is replaced by a suitable rule.
• The complete derivation in this case is processed in the rightmost way.

The string is “b a a b a a a b a”.

$\begin{array}{c}\text{G }\to \text{ As }\underset{\_}{\text{S}}\\ \to \text{ As b As b As }\underset{\_}{\text{S}}\\ \to \text{ As b As b As b As b As }\underset{\_}{\text{S}}\\ \to \text{ As b As b As b As b }\underset{\_}{\text{As}}\end{array}$

    $\begin{array}{c}\to \text{ As b As b As b }\underset{\_}{\text{As}}\text{ b}\\ \to \text{ As b As b }\underset{\_}{\text{As}}\text{ b b}\\ \to \text{ As b As�}\end{array}$