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In terms of the pumping lemma, the string abcd is broken into an portion a, a portion bc and a portion d. As a side remark, the problem of checking whether a given string can be accepted by a given nondeterministic finite automaton without visiting any state repeatedly, is NP hard.
In computer science, in particular in formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, [1] is a lemma that gives a property shared by all context-free languages and generalizes the pumping lemma for regular languages. The pumping lemma can be used to construct a refutation by ...
The pumping lemma can't be used to prove that a given Language L is regular, since it provides a necessary, but not sufficient condition for regularity; cf. the "⇒" after "regular(L)" in the formal expression, and section Pumping_lemma_for_regular_languages#Converse_of_lemma_not_true. - Jochen Burghardt 08:47, 14 June 2023 (UTC)
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
The proof is essentially the same as the standard pumping lemma: use the pigeonhole principle to find copies of some nonterminal symbol in the longest path in the shortest derivation tree. Now we prove the first part of Parikh's theorem, making use of the above lemma.
Ogden's lemma is often stated in the following form, which can be obtained by "forgetting about" the grammar, and concentrating on the language itself: If a language L is context-free, then there exists some number (where p may or may not be a pumping length) such that for any string s of length at least p in L and every way of "marking" p or more of the positions in s, s can be written as
1.1 Pumping Lemma. 2 comments. 1.2 Analytic injective functions on the extended complex plane. 3 comments. 1.3 Lie Groups and Infinitesimal Actions. 4 comments.
Computability is the ability to solve a problem in an effective manner. ... and won't be detailed here. There exists a Pumping lemma for context-free languages. An ...