If language L is regular, there exists an integer n such that,
for any word z in L, |z|>n,
there exist u,v,w with z = uvw, v nonempty, |vw|←n,
such that: uvkw ∈ L, for all k≥0
If language L is context-free, there exist integers p and q such that,
for any z in L, with |z|>p,
there exist u,v,w,x,y with z = uvwxy, v and x nonempty, |vwx|←q,
such that: uvkwxky ∈ L, for all k≥0
The conditions are used in constructing algorithms for decision problems about regular and context-free grammars, and in proving certain languages are not regular or are not context-free.
"pumping lemmas." A Dictionary of Computing. . Encyclopedia.com. (December 10, 2018). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/pumping-lemmas
"pumping lemmas." A Dictionary of Computing. . Retrieved December 10, 2018 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/pumping-lemmas
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.