# Pumping Lemma - The Blue World

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4:40. 58. Jahovea Water Pumping. Johnny Osbourne. the pumping lemma, Myhill-Nerode. relations.

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A regular grammar can be constructed to exactly generate the strings in a language. A regular expression can be constructed to exactly generate the strings in a language. Principle of Pumping Lemma The Pumping Lemma is made up of two words, in which, the word pumping is used to generate many input strings by pushing the symbol in input string one after another, and the word Lemma is used as intermediate theorem in a proof. Pumping lemma is a method to prove that certain languages are not context free. How to use the Pumping Lemma to prove that a language is not regular? The pumping lemma is most useful when we want to prove that a language is not regular, We do this by using a proof by contradiction. To prove that a given language L is not regular: 1.

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Using Pumping Lemma Proving the a language A is not regular using pumping lemma: 1. Assume that A is regular in order to obtain a contradiction 2. The pumping lemma guarantees the existence of a pumping length p so that all strings of length p or greater in A can be pumped 3. Find s A, |s| p, that cannot be pumped: demonstrate that s cannot be $\begingroup$ I'm not sure to fully understand what your first part is aboutWhen proving that a language is not regular, you assume that it satisfies the pumping lemma, and then show a contradiction.

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Closure under union.

Computability theory: -Turing machines -Church-Turing thesis -Decidability of problems/languages -Halting problem -Recursion theorem
Prove whether a language is or isn't regular or context-free by using the Pumping Lemma.

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If L is a context-free language, there is a pumping length p such that any string w ∈ L of length ≥ p can be written as w = uvxyz, where vy ≠ ε, |vxy| ≤ p, and for all i ≥ 0, uv i xy i z ∈ L.. Applications of Pumping Lemma.

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CC BY-SA 4.0. Bird scan lemma 60 The pumping lemma Låt L vara ett reguljärt språk som innehåller oändligt många strängar.

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So, the Pumping Lemma must hold. Define p to be the pumping length given by the Pumping Lemma. Choose s (often in terms of p). Because s ∈ L and |s| ≥ p, PL guarantees that s can be split into 3 pieces, s = xyz, where for any i ≥ 0, xy iz ∈ L. For all possible values of y (given the conditions of the Pumping Lemma), show that pumping xyiz is Notes on Pumping Lemma Finite Automata Theory and Formal Languages { TMV027/DIT321 Ana Bove, March 5th 2018 In the course we see two di erent versions of the Pumping lemmas, one for regular languages and one for context-free languages.