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More Concise Representation of Regular Languages by Automata and Regular Expressions

  • Viliam Geffert
  • Carlo Mereghetti
  • Beatrice Palano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)

Abstract

We consider two formalisms for representing regular languages: constant height pushdown automata and straight line programs for regular expressions. We constructively prove that their sizes are polynomially related. Comparing them with the sizes of finite state automata and regular expressions, we obtain optimal exponential and double exponential gaps, i.e., a more concise representation of regular languages.

Keywords

Pushdown automata regular expressions straight line programs descriptional complexity 

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References

  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)MATHGoogle Scholar
  2. 2.
    Brüggemann-Klein, A.: Regular expressions into finite automata. Theoretical Computer Science 120, 197–213 (1993)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Caron, P., Ziadi, D.: Characterization of Glushkov automata. Theoretical Computer Science 233, 75–90 (2000)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Chandra, A., Kozen, D., Stockmeyer, L.: Alternation. J. ACM 28, 114–133 (1981)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Ehrenfeucht, A., Zieger, P.: Complexity measures for regular expressions. J. Computer and System Sciences 12, 134–146 (1976)MATHGoogle Scholar
  6. 6.
    Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (2001)MATHGoogle Scholar
  7. 7.
    Kleene, S.: Representation of events in nerve nets and finite automata. In: Shannon, C., McCarthy, J. (eds.) Automata Studies, pp. 3–42. Princeton University Press, Princeton (1956)Google Scholar
  8. 8.
    Meyer, A.R., Fischer, M.J.: Economy of description by automata, grammars, and formal systems. In: IEEE 12th Symp. Switching and Automata Theory, pp. 188–191 (1971)Google Scholar
  9. 9.
    Rabin, M.: Probabilistic automata. Information and Control 6, 230–245 (1963)CrossRefGoogle Scholar
  10. 10.
    Rabin, M., Scott, D.: Finite automata and their decision problems. IBM J. Res. Develop. 3, 114–125 (1959)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Shepherdson, J.C.: The reduction of two–way automata to one–way automata. IBM J. Res. Develop. 3, 198–200 (1959)MathSciNetGoogle Scholar
  12. 12.
    Valiant, L.G.: Regularity and related problems for deterministic pushdown automata. J. ACM 22, 1–10 (1975)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Viliam Geffert
    • 1
  • Carlo Mereghetti
    • 2
  • Beatrice Palano
    • 2
  1. 1.Department of Computer ScienceP. J. Šafárik UniversityKošiceSlovakia
  2. 2.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly

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