Answered: Prove that C = {w|w has an equal number…

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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Question

Prove that C = {w|w has an equal number of 0s and 1s} is not regular. Consider
the string s=0p1p.

Expert Solution

The pumping lemma

If A is a regular language, then there is a number p (the pumping length) where if s is any string in A of length at least p, then s may be divided into three pieces, s = xyz, satisfying the following conditions:

for each i $\geq$ 0, $x y^{i} z \in A,$
$|y| > 0$ , and
$|x y| \leq p$ .

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