Skip to main content
SpringerLink
Log in

On reducing the number of stack symbols in a PDA

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

Two transformations are presented which, for any pushdown automaton (PDA)M withn states andp stack symbols, reduce the number of stack symbols to any desired numberp′ greater than one. The first transformation preserves deterministic behavior and produces an equivalent PDA witho(np/p′) states. The second construction, using a technique which introduces nondeterminism, produces an equivalent PDA withO(n√p/p′) states. Both transformations are essentially optimal, the former among determinism-preserving transformations, the latter among all transformations.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Goldstine, C. M. R. Kintala, and D. Wotschke. On measuring nondeterminism in regular languages.Information and Computation, 86:179–194, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Goldstine, J. K. Price, and D. Wotschke. On reducing the number of states in a pda.Mathematical Systems Theory, 15:315–321, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Goldstine, J. K. Price, and D. Wotschke. A pushdown automaton or a context-free grammar—which is more economical?Theoretical Computer Science, 18:33–40, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  4. S. Greibach. An infinite hierarchy of context-free languages.Journal of the ACM, 14:91–106, 1966.

    Google Scholar 

  5. J. Hartmanis.On the Succinctness of Different Representations of Languages. Lecture Notes in Computer Science, vol. 71. Springer-Verlag, Berlin, pp. 282–288, 1979.

    Google Scholar 

  6. J. Hartmanis. On Gödel speed-up and succinctness of language representations.Theoretical Computer Science, 26:335–342, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  7. C. M. R. Kintala and D. Wotschke. Amount of nondeterminism in finite automata.Acta Informatica, 13:199–204, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. R. Meyer and M. J. Fischer. Economy of description by automata, grammars, and formal systems.Proc. 12th Symposium on Switching and Automata Theory, pp. 188–191, 1981.

  9. E. M. Schmidt and T. G. Szymanski. Succinctness of descriptions of unambiguous context-free languages.SIAM Journal on Computing, 6:547–553, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. E. Stearns. A regularity test for pushdown machines.Information and Control, 11:323–340, 1967.

    Article  MATH  Google Scholar 

  11. L. G. Valiant. Regularity and related problems for deterministic pushdown automata.Journal of the ACM, 22:1–10, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  12. L. G. Valiant. A note on the succinctness of descriptions of deterministic languages.Information and Control, 32:139–145, 1976.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, The Pennsylvania State University, 16802, University Park, PA, USA

    Jonathan Goldstine

  2. Bell Laboratories, 07733, Holmdel, NJ, USA

    John K. Price

  3. Fachbereich Informatik, Johann Wolfgang Goethe-Universität, Frankurt, Federal Republic of Germany

    Detlef Wotschke

Authors
  1. Jonathan Goldstine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John K. Price
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Detlef Wotschke
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by the National Science Foundation under Grants MCS 76-10076 and MCS 76-10076A01 and by the Stiftung Volkswagenwerk under Grant No. II/62 325.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goldstine, J., Price, J.K. & Wotschke, D. On reducing the number of stack symbols in a PDA. Math. Systems Theory 26, 313–326 (1993). https://doi.org/10.1007/BF01189852

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01189852

Keywords

Search

Navigation