Pumping Lemma

Question

Answer 1

 Firstly Pumping Lemma is Negativity test .

 If L is context-free then L satisfies the pumping lemma. .

Assume PL for CFL's  If L fails in Pumping lemma test then definitely the L is NOT CFL

If L doesn't fail in PL test then we cannot assure it belongs to CFL or not.

Here L2 is not CF == > L2 pass or fail PL test

$a^{n}b^{n}c^{n}$ is not CFL since it doesnot satisfy PL.

Given L1 is CFL==> L satisfy PL test.

$a^{n}b^{n}$ satisfies PL and is CFL.

option C.

there may be some  non-CFL but satisfies PL for CFL . 

http://cs.stackexchange.com/questions/12041/example-of-a-non-context-free-language-that-nonetheless-can-be-pumped

Comments

what about (C)

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corrected Thanks monty

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NIce, Explain.

Answer 2

Option C.

Pumping Lemma is  a negativity test, means it can say if a Language is NOT CFL but cannot that say it IS CFL.

A Language(L) satisfying pumping lemma for CFL may/may not be a CFL. But, if L does not satisfy pumping lemma for CFL then it is surely non CFL.

In other words, if it is pumping lemma for CFL then  All CFL’s will satisfy it plus other language may also satisfy it.

Similarly, if it is pumping lemma for regular, then All regular language will satisfy it plus other language may also satisfy it.