Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

An infinite hierarchy of intersections of context-free languages

  • 95 Accesses

  • 32 Citations

Abstract

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.

This is a preview of subscription content, log in to check access.

References

  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.

  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.

  3. [3]

    J. Evey, “The Theory and Application of Pushdown Store Machines”, Harvard University Doctoral Thesis, 1963.

  4. [4]

    S. Ginsburg,The Mathematical Theory of Context-Free Languages, McGraw-Hill, New York, 1966.

  5. [5]

    S. Ginsburg andE. H. Spanier, Bounded ALGOL-like languages,Trans. Amer. Math. Soc. 113 (1964), 333–368.

  6. [6]

    S. Ginsburg andE. H. Spanier, Semigroups, Presburger formulas and languages,Pacific J. Math. 16 (1966), 285–296.

  7. [7]

    S. Y. Kuroda, Classes of languages and linear bounded automata,Information and Control 7 (1964), 207–223.

  8. [8]

    J. Myhill, “Linear bounded automata”,WADD Tech. Note, No. 60-165 Wright Patterson Air Force Base, Ohio, 1960.

  9. [9]

    R. J. Parikh, “Language generating devices”, M.I.T. Res. Lab. Electron Quart Prog. Rept. 60, 1961, pp. 199–212.

  10. [10]

    Leonard Y. Liu, “Finite-Reversal Pushdown Automata,” Ph.D. Dissertation, Princeton University, 1968, pp. 62–63.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Liu, L.Y., Weiner, P. An infinite hierarchy of intersections of context-free languages. Math. Systems Theory 7, 185–192 (1973). https://doi.org/10.1007/BF01762237

Download citation

Keywords

  • Computational Mathematic
  • Infinite Hierarchy