Select the correct alternative from the given choices. The...

Select the correct alternative from the given choices. The language $L$, is defined as set of strings that start and end with equal number of a's and contain any number of b's. The grammar $L(G)$ for language $L$ is defined with productions as: (A) $S \rightarrow a B a$ $B \rightarrow \varepsilon \mid b B$ (B) $S \rightarrow a B$ $B \rightarrow a \mid b B$ (C) $S \rightarrow a T \mid b S$ $T \rightarrow a T|b T| a \mid b$ (D) $S \rightarrow \mathrm{B} \mid a \mathrm{Sa}$ $B \rightarrow \varepsilon \mid b B$

Select the correct alternative from the given choices.
The language $L$, is defined as set of strings that start and end with equal number of a's and contain any number
of b's. The grammar $L(G)$ for language $L$ is defined with productions as:
(A) $S \rightarrow a B a$
$B \rightarrow \varepsilon \mid b B$
(B) $S \rightarrow a B$
$B \rightarrow a \mid b B$
(C) $S \rightarrow a T \mid b S$
$T \rightarrow a T|b T| a \mid b$
(D) $S \rightarrow \mathrm{B} \mid a \mathrm{Sa}$
$B \rightarrow \varepsilon \mid b B$

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Key Concepts

Balanced Language Constructs

Balanced language constructs refer to the idea of producing strings with matching or equal occurrences of specific symbols, often by using recursive grammatical rules. This concept is common in formal language theory for generating patterns like balanced parentheses or symmetric strings, where the pattern at the beginning mirrors the pattern at the end.

Recursive Productions

Recursive productions in grammars involve rules where a nonterminal symbol appears on the right-hand side of its own production. This recursion enables the generation of arbitrarily long or nested structures, such as strings with balanced patterns or matching pairs, which is crucial for constructing languages with symmetric patterns.

Context-Free Grammar

A context?free grammar (CFG) is a formal system that defines a language by specifying production rules, which replace symbols with other symbols. CFGs are fundamental in computer science for defining the syntax of programming languages and other formally structured languages.

Production Rules

Production rules are the definitions given in a grammar that describe how terminal and nonterminal symbols can be combined to form strings. They are used to generate all the valid strings in a language, and the structure of these rules determines the properties of the generated language.

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