proving languages not regular using Pumping Lemma

If L is a regular language then there is an integer n > 0 with the property that: (*) for any string x ? L where

? n

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Languages That Are and Are Not Regular

Prove that each of the following languages is not regular. . 02n n

Solution (verbose): Let F be the language 0?. Let x and y be arbitrary strings in F. Then x = 0i and y = 0j for some non-negative integers i = j.

Prove that each of the following languages is not regular. . 02n n

Prove that each of the following languages is not regular. . 02n n ? 0 Solution (concise): For any non-negative integers i = j the strings 02i.

Homework 4

Prove that the following languages are not regular. Suppose that language A is recognized by an NFA N and language B is the collection of strings not ...

1 Introduction 2 Reductions

It is about Different Ways to Prove a Language is Not regular. {af(n) : n ? N} is regular iff f is a finite variant of a function of the form.

Theorem 1. The language L = {a k : k is a perfect square} is not

Proof. Assume for the sake of contradiction that L is regular. By the Pump- ing Lemma for Regular Languages (PLRL) there exists a positive constant n.

4.1.2 Prove that the following are not regular languages. There are a

(b) {0n

. (a) Prove that the following languages are not regular by providing

Thus F is a fooling set for L. Because F is infinite

SIMPLICITY OF An 1. Introduction A finite group is called simple

When n ? 3 the group Sn is not simple since it has the normal subgroup An Proof. That the 3-cycles generate An for n ? 3 has been seen earlier in the ...