Mathematical systems theory

, Volume 7, Issue 2, pp 185–192 | Cite as

An infinite hierarchy of intersections of context-free languages

  • Leonard Y. Liu
  • Peter Weiner


The class of languages expressible as the intersection ofk context-free languages is shown to be properly contained within the class of languages expressible as the intersection ofk + 1 context-free languages. Hence an infinite hierarchy of classes of languages is exhibited between the class of context-sensitive languages and the class of context-free languages.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Y. Bar-Hillel, M. Perles andE. Shamir, On formal properties of simple phrase structure grammars,Z. Phonetik Sprachwiss. Kommunikat. 14 (1961), 142–172.Google Scholar
  2. [2]
    N. Chomsky andM. P. Schützenberger, The algebraic theory of context-free languages,Computer Programming and Formal Systems, North Holland, Amsterdam, 1963, pp. 118–161.Google Scholar
  3. [3]
    J. Evey, “The Theory and Application of Pushdown Store Machines”, Harvard University Doctoral Thesis, 1963.Google Scholar
  4. [4]
    S. Ginsburg,The Mathematical Theory of Context-Free Languages, McGraw-Hill, New York, 1966.Google Scholar
  5. [5]
    S. Ginsburg andE. H. Spanier, Bounded ALGOL-like languages,Trans. Amer. Math. Soc. 113 (1964), 333–368.Google Scholar
  6. [6]
    S. Ginsburg andE. H. Spanier, Semigroups, Presburger formulas and languages,Pacific J. Math. 16 (1966), 285–296.Google Scholar
  7. [7]
    S. Y. Kuroda, Classes of languages and linear bounded automata,Information and Control 7 (1964), 207–223.Google Scholar
  8. [8]
    J. Myhill, “Linear bounded automata”,WADD Tech. Note, No. 60-165 Wright Patterson Air Force Base, Ohio, 1960.Google Scholar
  9. [9]
    R. J. Parikh, “Language generating devices”, M.I.T. Res. Lab. Electron Quart Prog. Rept. 60, 1961, pp. 199–212.Google Scholar
  10. [10]
    Leonard Y. Liu, “Finite-Reversal Pushdown Automata,” Ph.D. Dissertation, Princeton University, 1968, pp. 62–63.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1973

Authors and Affiliations

  • Leonard Y. Liu
    • 1
  • Peter Weiner
    • 2
  1. 1.International Business Machines CorporationYorktown HeightsUSA
  2. 2.Department of Computer ScienceYale UniversityNew HavenUSA

Personalised recommendations