Formal Languages and Automata TheoryGive context-free grammars that generate the following languages. In all parts, thealphabet Σ is {0,1} a. {w| w contains at least three 1s}b. {w| w starts and ends with the same symbol}c. {w| the length of w is odd}Ad. {w| the length of w is odd and its middle symbol is a 0}e. {w| w = wR, that is, w is a palindrome}f. The empty set ·Give context-free grammars that generate the following languages. In all parts, thealphabet E is {0,1}.Aa. {w| w contains at least three 1s}b. {w| w starts and ends with the same symbol}c. {w| the length of w is odd}Ad. {w| the length of w is odd and its middle symbol is a 0}e. {w| w = w*, that is, w is a palindrome}f. The empty setR

Context Free Grammar for a) S -> R1R1R1R R -> 0R|1R|ϵ Context Free Grammar for b) S ->…

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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

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Formal Languages and Automata Theory

Give context-free grammars that generate the following languages. In all parts, the
alphabet Σ is {0,1}

a.
{w| w contains at least three 1s}
b. {w| w starts and ends with the same symbol}
c. {w| the length of w is odd}
Ad. {w| the length of w is odd and its middle symbol is a 0}
e. {w| w = w
R, that is, w is a palindrome}
f. The empty set

·Give context-free grammars that generate the following languages. In all parts, the
alphabet E is {0,1}.
Aa. {w| w contains at least three 1s}
b. {w| w starts and ends with the same symbol}
c. {w| the length of w is odd}
Ad. {w| the length of w is odd and its middle symbol is a 0}
e. {w| w = w*, that is, w is a palindrome}
f. The empty set
R

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