pumping lemma meaning: definition, quotations

pumping lemma

noun

Computer, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Science, Sciences A lemma which states that for a language to be a member of a language class any sufficiently long string in the language contains a section that can be removed or repeated any number of times with the resulting string remaining in the language, used to determine if a particular language is in a given language class (e.g. not regular).

There is a pumping lemma for CFLs similar to the one for regular sets. It can be used in the same way to show that certain sets are not context-free.1997, Dexter Kozen, Automata and computability, page 148:
In the literature one finds many pumping lemmas which describe the ability to repeat (pump) certain words repeatedly in some languages, under different circumstances.2002, Alejandro Maass, Servet Martínez, Jaime San Martín, Dynamics and randomness, page 174:

1 more example

String-language hierarchies are usually proven using formalism-specific pumping lemmata.2010, Marco Kuhlmann, Dependency Structures and Lexicalized Grammars: An Algebraic Approach, page 107: