Limits of exact algorithms for inference of minimum size finite state machines

  • Arlindo L. Oliveira
  • Stephen Edwards
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1160)


We address the problem of selecting the minimum sized finite state machine consistent with given input/output samples. The problem can be solved by computing the minimum finite state machine equivalent to a finite state machine without loops obtained from the training set. We compare the performance of four algorithms for this task: two algorithms for incompletely specified finite state machine reduction, an algorithm based on a well known explicit search procedure and an algorithm based on a new implicit search procedure that is introduced in this paper.


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  1. 1.
    D. Angluin. On the complexity of minimum inference of regular sets. Inform. Control, 39(3):337–350, 1978.CrossRefGoogle Scholar
  2. 2.
    D. Angluin. Learning regular sets from queries and counterexamples. Inform. Comput., 75(2):87–106, November 1987.CrossRefGoogle Scholar
  3. 3.
    A. W. Biermann and R. Krishnaswamy. Constructing programs from example computations. IEEE Trans. on Software Engineering, SE-2:141–153, 1976.Google Scholar
  4. 4.
    A. W. B. R. I. Biermann and F. E. Petry. Speeding up the synthesis of programs from traces. IEEE Trans. on Computers, C-24:122–136, 1975.Google Scholar
  5. 5.
    R. E. Bryant. Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers, 35:677–691, 1986.Google Scholar
  6. 6.
    M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York, 1979.Google Scholar
  7. 7.
    E. M. Gold. Complexity of automaton identification from given data. Inform. Control, 37:302–320, 1978.Google Scholar
  8. 8.
    G. Hachtel, J.-K. Rho, F. Somenzi, and R. Jacoby. Exact and heuristic algorithms for the minimization of incompletely specified state machines. In The Proceedings of the European Design Automation Conference, 1991.Google Scholar
  9. 9.
    T. Kam and R.K. Brayton. Multi-valued decision diagrams. Tech. Report No. UCB/ERL M90/125, December 1990.Google Scholar
  10. 10.
    T. Kam, T. Villa, R. K. Brayton, and A. Sangiovanni Vincentelli. A fully implicit algorithm for exact state minimization. Proc. Design Automat. Conf., 1994.Google Scholar
  11. 11.
    Arlindo L. Oliveira and Stephen A. Edwards. Inference of state machines from examples of behavior. Technical report, UCB/ERL Technical Report M95/12, Berkeley, CA, 1995.Google Scholar
  12. 12.
    L. Pitt and M. Warmuth. The minimum consistent DFA problem cannot be approximated within any polynomial. J. ACM, 40(1):95–142, 1993.Google Scholar
  13. 13.
    S. Porat and J. A. Feldman. Learning automata from ordered examples. In Proc. 1st Annu. Workshop on Comput. Learning Theory, pages 386–396, San Mateo, CA, 1988. Morgan Kaufmann.Google Scholar
  14. 14.
    R. E. Schapire. The Design and Analysis of Efficient Learning Algorithms. MIT Press, Cambridge, MA, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Arlindo L. Oliveira
    • 1
  • Stephen Edwards
    • 2
  1. 1.Cadence European Laboratories/INESC-ISTLisboaPortugal
  2. 2.UC BerkeleyBerkeleyUSA

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