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In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages. Informally, it says that all sufficiently long strings in a regular language may be pumped —that is, have a middle section of the string repeated an arbitrary number of times—to produce a new ...
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)
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
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
Joseph and Young introduced a class of NP-complete problems, the k-creative sets, for which no p-isomorphism to the standard NP-complete problems is known. [10] Kurtz et al. showed that in oracle machine models given access to a random oracle , the analogue of the conjecture is not true: if A is a random oracle, then not all sets complete for ...
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.
In fact, when used within information retrieval systems, stemming improves query recall accuracy, or true positive rate, when compared to lemmatization. Nonetheless, stemming reduces precision, or the proportion of positively-labeled instances that are actually positive, for such systems. [5] For instance: The word "better" has "good" as its lemma.