A more general form of this result is called the Pumping lemma for regular languages, which can be used to show that broad classes of languages cannot be recognized by a finite state machine.
12.
The set of all infinite words over " A " whose " b " form blocks of prime length is not sofic ( this can be shown by using the pumping lemma ).
13.
Finite languages ( which are regular and hence context-free ) obey the pumping lemma trivially by having " p " equal to the maximum string length in " L " plus one.
14.
Moreover, the pumping lemma guarantees that the length of " xy " will be at most " p ", imposing a limit on the ways in which " w " may be split.
15.
The paper's contribution lies in its proof of a probabilistic generalization of the pumping lemma, a device used in theoretical computer science as a necessary condition for a language to be described by only a finite number of states.
16.
I remember spending a few hours on one pumping lemma problem once and finally finding a complicated but correct counterexample . ( The prof . hadn't intended the question to be so hard and replaced it after I had completed it.
17.
Are there examples of languages which can be proven to be non-CFLs with Ogden's lemma, but not with the pumping lemma and closure of CFLs under regular intersection and gsm mappings ?-- talk ) 10 : 51, 13 June 2011 ( UTC)
18.
The pumping lemma is often used to prove that a given language " L " is non-context-free, by showing that arbitrarily long strings " s " are in " L " that cannot be " pumped " without producing strings outside " L ".
19.
:How to " solve a proof " is a bit vague, but I think you mean to ask how one uses the pumping lemma to show that a given language is " not " regular . ( The pumping lemma doesn't show a language " is " regular; it can only be used to prove that no finite state automaton can accept a particular language, for if one existed, the pumping lemma would apply . ) These lecture notes are decent and provide a number of examples starting at " Applications ".
20.
:How to " solve a proof " is a bit vague, but I think you mean to ask how one uses the pumping lemma to show that a given language is " not " regular . ( The pumping lemma doesn't show a language " is " regular; it can only be used to prove that no finite state automaton can accept a particular language, for if one existed, the pumping lemma would apply . ) These lecture notes are decent and provide a number of examples starting at " Applications ".
