Steps of a “Pumping Lemma” Proof Nonmechanical elements of a “pumping lemma”-based nonregularity proof Choose x of length at least n. Choose m (often 0 or 2, never 1) Derive the contradiction Some examples: L 1 = {a i | i is a square} ...
The two most important examples are thepumping lemma for regular languagesand thepumping lemma for context-free languages.Ogden's lemmais a second, stronger pumping lemma forcontext-free languages. Theselemmascan be used to determine if a particular language isnotin a given language class. However...
we show that a pumping lemma for a class of languagesCCcan be used to study the computational complexity of the predicate “∈CC” via highly efficient many-one reductions. In this paper, we use extended regular expressions (EXREGs, introduced in Câmpeanu et al...
F-systemFormal languagePumping lemmaGeometric folding processes are ubiquitous in natural systems ranging from protein biochemistry to patterns of insect wings and leaves. In a previous study, a folding operation between strings of formal languages was introduced as a model of such processes. The ...
A Pumping Lemma for Context-Free Graph Languages Each sufficiently large graph belonging to a context-free graph language (generated by an edge-replacement system) can be decomposed in three subgraphs FIRST, LINK and LAST, such that a suitable chain gluing of FIRST, LAST and N examples... ...
Proofs using the new lemma are typically more elegant, because they usually do not involve the messy analysis of possible patterns for y in the rewriting w=xyz. In the article, we first present an elementary proof of the non-pumping lemma, and then give examples showing how the lemma can ...
Note that by using a grammar or a recursive system the languages in our 12sexamples are generated in a quite nondeterministic way. Finally we mention that for the context-free languages and a...D. S. Wise. A strong pumping lemma for context{free languages. Theoret. Comp. Sci., 3:359...
Our experience shows that the examples and tutor-driven discussions helped students to reveal typical reasoning obstacles related to Pumping Lemma for regular languages. As a continuation of this effort, we have developed similar examples for teaching of Pumping Lemma for context-free languages.Judith ...
Instances such as 16/64 and 19/95 are well-known. In this paper, we consider such "weird fractions" and show how examples of them can be multiplied ad infinitum and lead to interesting questions.doi:10.4169/074683410X521955Michael N. Fried and Mayer Goldberg...
We provide a collection of examples to illustrate the usage of the Generalized Non-Pumping Lemma, and show a specific example which is easy to demonstrate its non-regularity this way, but we have not yet found a way to show its non-regularity using conventional means....