Mathematical systems theory

, Volume 21, Issue 1, pp 223–233 | Cite as

Comparisons between some pumping conditions for context-free languages

  • R. Hewett
  • G. Slutzki


We present a systematic investigation of the relationships between various pumping properties—the classic pumping condition of Bar-Hillelet al., Ogden's condition, a generalized Ogden condition of Bader and Moura, Sokolowski's condition, an extended Sokolowski condition of Grant, and linear versions of some of these conditions. We define special language operations that allow us to produce, in a systematical and uniform way, languages that satisfy some combinations of the pumping conditions but not the others. We show, among others, that the general and the linear pumping conditions are “orthogonal,” whereas the generalized Ogden condition is stronger than the extended Sokolowski condition.


Distinguished Position Linear Version Formal Language Theory Phrase Structure Grammar Simple Phrase Structure 
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Copyright information

© Springer-Verlag New York Inc 1988

Authors and Affiliations

  • R. Hewett
    • 1
  • G. Slutzki
    • 2
  1. 1.Knowledge Systems Laboratory, Department of Computer ScienceStanford UniversityStanfordUSA
  2. 2.Department of Computer ScienceIowa State UniversityAmesUSA

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