Let >= {a,b}. For the language L defined by each of the following grammars, list the first tenelements of L in lexicographic order (shortest first, then alphabetically if same length), and thenindicate whether or not L is regular. (4) S -> aSS-> aSbSS-> €E, a, aa, ab, aaa, aab, aba, aaaa, aaab, aaba and L is regular.€, a, aa, ab, aaa, aab, aba, aaaa, aaab, aaba and L is not regular.a, aa, ab, aaa, aab, aba, aaaa, aaab, aaba, aabb and L is regular.a, aa, ab, aaa, aab, aba, aaaa, aaab, aaba, aabb and L is not regular.

Answered: (4) S-> as S-> aSbS S-> € O €, a, aa,…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Let >= {a,b}. For the language L defined by each of the following grammars, list the first ten
elements of L in lexicographic order (shortest first, then alphabetically if same length), and then
indicate whether or not L is regular.

(4) S -> aS
S-> aSbS
S-> €
E, a, aa, ab, aaa, aab, aba, aaaa, aaab, aaba and L is regular.
€, a, aa, ab, aaa, aab, aba, aaaa, aaab, aaba and L is not regular.
a, aa, ab, aaa, aab, aba, aaaa, aaab, aaba, aabb and L is regular.
a, aa, ab, aaa, aab, aba, aaaa, aaab, aaba, aabb and L is not regular.

Expert Solution

Step 1: Introduction:

Context-Free Grammar:

A CFG, or Context-Free Grammar, is a formal grammar used in formal language theory and theoretical computer science to describe the syntax or structure of context-free languages. It consists of a set of production rules that define how strings in a language can be generated or derived.

A CFG typically includes the following components:

A set of terminal symbols (Σ): These are the basic symbols of the language that appear in the strings generated by the grammar. Terminal symbols are also called "tokens" or "terminal characters" and are typically the characters of the alphabet used in the language.
A set of non-terminal symbols (N): These are symbols that represent syntactic categories or placeholders for groups of terminal symbols. Non-terminal symbols are used to create more complex structures in the language.
A start symbol (S): This is a special non-terminal symbol from which the derivation of strings begins. It represents the highest-level syntactic category in the language.
A set of production rules (or productions): These rules specify how non-terminal symbols can be replaced by other symbols (terminals or non-terminals) in a step-by-step manner. Each production rule typically takes the form of a non-terminal symbol followed by an arrow (→) and a sequence of terminals and non-terminals.

A context-free grammar defines a context-free language, which is a type of formal language that can be recognized by a context-free parser or a pushdown automaton. Context-free grammars are widely used in programming language design, parsing, and the specification of the syntax of programming languages. They are also used in various other areas of theoretical computer science and linguistics.

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