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Theorem :- Let M=(Q,S,δ,q0,F) be an Finite Automate and has n number of states. Let L be the regular language accepted by M .Let for every string x in L, there exists a constant n such that |x|>=n. Now , if the string x can be broken into three sub strings u,v and w such that

x=uvw

satisfying the following constraints :

1. v≠ ɛ i.e., |v|>=0

2. |uv|<= n

then uv1w is in L for i>=0

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Q: State and prove pumping lemma for regular languages?
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The pumping lemma is a tool used in formal language theory to show that certain languages are not context-free. By applying the pumping lemma to a language and finding a contradiction, it can be demonstrated that the language is not context-free.


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To use the pumping lemma to prove that a language is not regular, you would assume the language is regular and then show that there is a string in the language that cannot be &quot;pumped&quot; according to the lemma's conditions. This contradiction would indicate that the language is not regular.


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