onsider the following context-free grammar:Give the four elements of this grammar{T,N,S,P} Show the parse tree that this grammar would assign to :!false or true and falseIs this grammar ambiguous? A-AA or AA and A!Atrue false

Answered: onsider the following context-free…

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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onsider the following context-free grammar:

Give the four elements of this grammar{T,N,S,P}
Show the parse tree that this grammar would assign to :!false or true and false
Is this grammar ambiguous?

Expert Solution

Step 1

The context-free languages are a larger set of languages than the regular languages that we have been studying so far. Context-free languages are particularly important because most programming languages are context-free.

Context-free languages are described by grammars. In this module, we will examine grammars, how they can be used to generate the strings of a language, and how they can be used to parse a string to see if it is in the language.

1) Answer :

A context-free grammar G=(V,T,P,S) is composed of

N : a set of Non-terminals (also known as variables), each denoting a set of strings.
T : a set of terminal symbols (“terminals” for short) that constitutes the alphabet over which the strings in the language are composed.
P : a set of productions, rules that recursively define the structure of the language.
- A production has the form A→α where
- A is a variable (one of the symbols in V).
  α is a string of zero or more symbols that may be either terminals or variables.
S : a starting symbol. This is a variable that denotes the set of strings comprising the entire language.

For the given grammar :

S → A
A → A+A | A*A | !A | true | false

G = ({A}, {true, false}, P, S)

P = {S → A, A → A+A | A*A | !A | true | false}

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