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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 1987: Foundations of Software Technology and Theoretical Computer Science pp 26–43Cite as

Relating the degree of ambiguity of finite automata to the succinctness of their representation

  • Session 1 Automata And Formal Languages
  • Conference paper
  • First Online:

  • 150 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 287))

Abstract

We consider the problem of how the size of a nondeterministic finite automaton (nfa) representing a regular language depends on the degree of ambiguity of the nfa. We obtain results for the unary and bounded inputs, and partial results for the unrestricted inputs. One of the main results of this paper shows that for unrestricted inputs, deterministic, unambiguous and nondeterministic machines form a hierarchy with respect to the number of states, solving an open problem of Stearns and Hunt. We also propose a new approach to the study of the succinctness of representation through regularity preserving closure properties and obtain some results in this direction.

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References

  1. Berman, P., A note on sweeping automata, ICALP 1979, pp. 91–97.

    Google Scholar 

  2. Chan, T. and O. Ibarra, On the finite-valuedness problem for sequential machines, Theoretical Computer Science, 1983, pp. 95–101.

    Google Scholar 

  3. Denes, J., K.H. Kim and F.W. Rouch, Automata on one symbol, Studies in Pure Mathematics 1985, pp. 127–134.

    Google Scholar 

  4. Ehrenfeucht, A. and P. Zeiger, Complexity measures for regular expressions, Journal of Computer and System Sciences, 12, 1976, pp. 134–146.

    Google Scholar 

  5. Eilenberg, S., Automata, Languages and machines, Vol. A, Academic Press, NY 1974.

    Google Scholar 

  6. Hopcroft J. and J. Ullman, Introduction to Automata Theory, Formal Languages and Computation, Addison-Wesley, 1979.

    Google Scholar 

  7. Ibarra, O. and B. Ravikumar, On sparseness, ambiguity and other decision problems for acceptors and transducers, Third Annual Symposium on Theoretical Aspects of Computer Science, Orsay, France, 1986, pp. 171–179.

    Google Scholar 

  8. Kintala C. and D. Wotschke, Amounts of nondeterminism in finite automata, Acta Informatica, 1980, pp. 199–204.

    Google Scholar 

  9. Kintala C. and D. Wotschke, Concurrent conciseness of degree, probabilistic, nondeterministic and deterministic finite automata, Fourth Symposium on Theoretical Aspects of Computer Science, 1986, pp. 291–305.

    Google Scholar 

  10. Kranakis, E., Primality and Cryptography, Yale University Technical Report, 1985.

    Google Scholar 

  11. Kuich, W., On the entropy of context-free languages, Information and Control, 1970, pp. 173–200.

    Google Scholar 

  12. Mandl, R., Precise bounds associated with the subset construction on various classes of nondeterministic finite automata, Seventh Princeton Conference on Information and System Science, 1973, pp. 263–267.

    Google Scholar 

  13. Meyer, A. and M. Fischer, Economy of description by automata, grammars, and formal Systems, Proc. of Twelfth IEEE Symposium on Switching and Automata Theory, 1971, pp. 188–191.

    Google Scholar 

  14. Moore, F., On the bounds for state-set size in the proofs of equivalence between nondeterministic and two-way automata, IEEE Transactions on Computers, 20, 1971, pp. 1211–1214.

    Google Scholar 

  15. Paul, W., Kolmogorov complexity and lower bounds, 2nd International Conference on Fundamentals of Computation Theory, 1979.

    Google Scholar 

  16. Rabin, M. and D. Scott, Finite automata and their decision problems, IBM Journal of Research and Development, 3, 1959, pp. 114–125.

    Google Scholar 

  17. Sakoda, W. and M. Sipser, Nondeterminism and the size of two-way finite automata, Proceedings of Tenth Annual ACM Symposium on Theory of Computing, 1978, pp. 275–286.

    Google Scholar 

  18. Schmidt, E., Succinctness of descriptions of context-free, regular and finite languages, Ph. D. Thesis, Cornell University, 1978.

    Google Scholar 

  19. Schmidt, E., (private communication).

    Google Scholar 

  20. Sipser, M., Lower bounds on the size of sweeping automata, Proc. of Eleventh Annual ACM Symposium on Theory of Computing, 1979, pp. 360–364.

    Google Scholar 

  21. Sipser, M., Halting space-bounded computations, Theoretical Computer Science, 1980, pp. 335–338.

    Google Scholar 

  22. Stearns, R. and H. Hunt, On the equivalence and containment problems for unambiguous regular expressions, regular grammars and finite automata, SIAM Journal of Computing, 14, 1985, pp. 598–611.

    Article  Google Scholar 

  23. Weber, A. and H. Seidl, On the degree of ambiguity of finite automata, Proc. of Math. Foundations of Comp. Science, 1986, pp. 620–629.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Minnesota, 55455, Minneapolis, Minnesota

    Oscar H. Ibarra & Bala Ravikumar

Authors
  1. Oscar H. Ibarra
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  2. Bala Ravikumar
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Editor information

Kesav V. Nori

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© 1987 Springer-Verlag Berlin Heidelberg

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Ibarra, O.H., Ravikumar, B. (1987). Relating the degree of ambiguity of finite automata to the succinctness of their representation. In: Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1987. Lecture Notes in Computer Science, vol 287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18625-5_40

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  • DOI: https://doi.org/10.1007/3-540-18625-5_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18625-0

  • Online ISBN: 978-3-540-48033-4

  • eBook Packages: Springer Book Archive

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