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Pumping lemma information


In the theory of formal languages, the pumping lemma may refer to:

  • Pumping lemma for regular languages, the fact that all sufficiently long strings in such a language have a substring that can be repeated arbitrarily many times, usually used to prove that certain languages are not regular
  • Pumping lemma for context-free languages, the fact that all sufficiently long strings in such a language have a pair of substrings that can be repeated arbitrarily many times, usually used to prove that certain languages are not context-free
  • Pumping lemma for indexed languages
  • Pumping lemma for regular tree languages

and 22 Related for: Pumping lemma information

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Pumping lemma

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context-free Pumping lemma for indexed languages Pumping lemma for regular tree languages Ogden's lemma, a stronger version of the pumping lemma for context-free...

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Pumping lemma for regular languages

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repeating y {\displaystyle y} zero or more times is known as "pumping". Moreover, the pumping lemma guarantees that the length of x y {\displaystyle xy} will...

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Tree automaton

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language L can be vertically tripartited such that arbitrary repetition ("pumping") of the middle part keeps the resulting term in L. For the language of...

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Pumping

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Look up pumping in Wiktionary, the free dictionary. Pumping may refer to: The operation of a pump, for moving a liquid from one location to another The...

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Chomsky hierarchy

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S → aSb S → ab The language is context-free but not regular (by the pumping lemma for regular languages). Type-1 grammars generate context-sensitive languages...

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List of lemmas

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Newman's lemma (term rewriting) Ogden's lemma Pumping lemma sometimes called the Bar-Hillel lemma Hotelling's lemma Shephard's lemma Cousin's lemma (integrals)...

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List of mathematical proofs

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proof Generating a vector space Linear independence Polynomial Proof Pumping lemma Simpson's rule Accumulation point Addition in N associativity of addition...

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Computability

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regular language. A more general form of this result is called the Pumping lemma for regular languages, which can be used to show that broad classes...

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Micha Perles

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Perles–Sauer–Shelah lemma, a result in extremal set theory whose proof was credited to Perles by Saharon Shelah. The pumping lemma for context-free languages...

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Ogden

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United Kingdom Government Actuary's Department Ogden's lemma, a generalization of the pumping lemma for context-free languages Justice Ogden (disambiguation)...

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List of formal language and literal string topics

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grammar Myhill-Nerode theorem Parsing expression grammar Prefix grammar Pumping lemma Recursively enumerable language Regular expression Regular grammar Regular...

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Chomsky normal form

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Backus–Naur form CYK algorithm Greibach normal form Kuroda normal form Pumping lemma for context-free languages — its proof relies on the Chomsky normal...

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Counter automaton

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ignored by F’s control makes it a counter automaton accepting L. by the pumping lemma for regular languages John E. Hopcroft and Jeffrey D. Ullman (1979)...

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Interchange lemma

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languages, the interchange lemma states a necessary condition for a language to be context-free, just like the pumping lemma for context-free languages...

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Regular language

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language is not regular, one often uses the Myhill–Nerode theorem and the pumping lemma. Other approaches include using the closure properties of regular languages...

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Regular expression

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language of squares is not regular, nor is it context-free, due to the pumping lemma. However, pattern matching with an unbounded number of backreferences...

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Automata theory

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of the number of states in a minimal machine for the language. The pumping lemma for regular languages, also useful in regularity proofs, was proven...

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Eli Shamir

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to full professor in 1972. Shamir was one of the discoverers of the pumping lemma for context-free languages. He did research in partial differential...

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Linear grammar

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intersection is not only not linear, but also not context-free. See pumping lemma for context-free languages. As a corollary, linear languages are not...

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Induction of regular languages

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that of k-reversible languages. Chomsky and Miller (1957) used the pumping lemma: they guess a part v of an input string uvw and try to build a corresponding...

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Pigeonhole principle

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{1}{M}}<e.} Variants occur in a number of proofs. In the proof of the pumping lemma for regular languages, a version that mixes finite and infinite sets...

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JFLAP

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grammar Proof on deterministic finite automaton to regular expression pumping lemma for regular languages Topics on context-free language include: pushdown...

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