arrow_forward Step 1 Context Free Grammar: A formal language that is used to generate all possible strings in a given formal language is called context free grammar. It can be defined as: G=(V, T, P, S) Where G specifies the grammar V specifies the finite set of non-terminal symbols. T specifies the finite set of terminal symbols. P specifies the set of production rules. S specifies the start symbol. The start symbol S is used to derive a string in a context free grammar. It is derived by repeatedly replacing a non-terminal symbol by the right-hand-side production until all the non-terminal symbols have been replaced by the terminal symbols. arrow_forward Step 2 G is a context-free grammar for a language L, and L contains only strings of length 2 or greater. We have to prove that there is a context-free grammar Gd which generates L such that every rule in Gd has the form A -> x1x2, where A is a terminal and each xi is a terminal or a non-terminal. Let the alphabet of the language L is {a} since none is given in the question. For string “aa”: By applying the production SaAa, A->E, we get the string “aa”. For string “aaa”” By applying the production SaAa, AaA, and then AE, we get the string “aaa”.

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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Step 1

Context Free Grammar:

A formal language that is used to generate all possible strings in a given formal language is called context free grammar. It can be defined as:

G=(V, T, P, S)

Where G specifies the grammar

V specifies the finite set of non-terminal symbols.

T specifies the finite set of terminal symbols.

P specifies the set of production rules.

S specifies the start symbol.

The start symbol S is used to derive a string in a context free grammar. It is derived by repeatedly replacing a non-terminal symbol by the right-hand-side production until all the non-terminal symbols have been replaced by the terminal symbols.

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Step 2

G is a context-free grammar for a language L, and L contains only strings of length 2 or greater. We have to prove that there is a context-free grammar G^d which generates L such that every rule in G^d has the form A -> x₁x₂, where A is a terminal and each x_i is a terminal or a non-terminal.

Let the alphabet of the language L is {a} since none is given in the question.

For string “aa”:

By applying the production SaAa, A->E, we get the string “aa”.

For string “aaa””

By applying the production SaAa, AaA, and then AE, we get the string “aaa”.

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