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Succinct Descriptions of Regular Languages with Binary ⊕-NFAs

  • Lynette van Zijl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2759)

Abstract

Champarnaud [1] analyzed the number of states obtained from a binary -NFA during the subset construction. We extend this work to an experimental analysis of the size of the minimal DFAs obtained from binary ⊕-NFAs.We then consider the number of distinct languages accepted by binary ⊕-NFAs, and compare that to Domaratzki’s results [2] for (traditional) binary NFAs. We also show that there are certain regular languages which are accepted by succinct ⊕-NFAs, but for which no succinct traditional NFA exists.

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References

  1. [1]
    Champarnaud, J., Hansel, G., Paranthoën, T., Ziadi, D.: NFAs bitstream-based random generation. In: Proceedings of the 4th Workshop on the Descriptional Complexity of Formal Systems, London, Ontario, Canada (2002)Google Scholar
  2. [2]
    Domaratzki, M., Kisman, D., Shallit, J.: On the number of distinct languages accepted by finite automata with n states. Journal of Automata, Languages and Combinatorics 7 (2002) 469–486zbMATHMathSciNetGoogle Scholar
  3. [3]
    Meyer, A., Fischer, M.: Economy of description by automata, grammars, and formal systems. In: Proceedings of the 12th Annual IEEE Symposium on Switching and Automata Theory, Michigan, IEEE (1971) 188–191CrossRefGoogle Scholar
  4. [4]
    van Zijl, L.: Nondeterminism and succinctly representable regular languages. In: Proceedings of SAICSIT’2002. ACM International Conference Proceedings Series, Port Elizabeth, South Africa (2002) 212–223Google Scholar
  5. [5]
    Golomb, S.: Shift Register Sequences. Holden-Day, Inc. (1967)Google Scholar
  6. [6]
    van Zijl, L.: Random number generation with ⊕-NFAs. In: Proceedings of the CIAA 2001. Volume 2494 of Lecture Notes in Computer Science., Pretoria, South Africa (2002) 263–273Google Scholar
  7. [7]
    Chaudhuri, P., Chowdhury, D., Nandi, S., Chattaopadhyay, S.: Additive Cellular Automata: Theory and Applications. Volume 1. IEEE Computer Society Press, Los Alamitos, California (1997)zbMATHGoogle Scholar
  8. [8]
    Sipser, M.: Introduction to the Theory of Computation. PWS Publishing Company, Boston (1997)Google Scholar
  9. [9]
    van Zijl, L.: Generalized Nondeterminism and the Succinct Representation of Regular Languages. PhD thesis, University of Stellenbosch, South Africa (1997)Google Scholar
  10. [10]
    Dornhoff, L., Hohn, F.: Applied Modern Algebra. MacMillan Publishing Co., Inc., New York (1977)Google Scholar
  11. [11]
    Stone, H.: Discrete Mathematical Structures and their Applications. Computer Science Series. Science Research Associates, Inc., Chicago (1973)zbMATHGoogle Scholar
  12. [12]
    van Zijl, L., Harper, J. P., Olivier, F.: The MERLin environment applied to ⋆-NFAs. In: Proceedings of the CIAA2000. Volume 2088 of Lecture Notes in Computer Science., London, Ontario, Canada (2001) 318–326Google Scholar
  13. [13]
    Raymond, D., Wood, D.: The user’s guide to Grail. Technical report, University of Waterloo, Waterloo, Canada (1995)Google Scholar
  14. [14]
    Chrobak, M.: Finite automata and unary languages. Theoretical Computer Science (1986) 149–158Google Scholar
  15. [15]
    Leiss, E.: Succinct representation of regular languages by boolean automata. Theoretical Computer Science 13 (1981) 323–330zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Lynette van Zijl
    • 1
  1. 1.Department of Computer ScienceStellenbosch UniversitySouth Africa

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