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Machine Learning

, Volume 44, Issue 1–2, pp 93–119 | Cite as

Efficient Algorithms for the Inference of Minimum Size DFAs

  • Arlindo L. Oliveira
  • João P.M. Silva
Article

Abstract

This work describes algorithms for the inference of minimum size deterministic automata consistent with a labeled training set. The algorithms presented represent the state of the art for this problem, known to be computationally very hard.

In particular, we analyze the performance of algorithms that use implicit enumeration of solutions and algorithms that perform explicit search but incorporate a set of techniques known as dependency directed backtracking to prune the search tree effectively.

We present empirical results that show the comparative efficiency of the methods studied and discuss alternative approaches to this problem, evaluating their advantages and drawbacks.

deterministic finite automata implicit enumeration search methods 

References

  1. Angluin, D. (1978). On the complexity of minimum inference of regular sets. Inform. Control, 39:3, 337–350.Google Scholar
  2. Angluin, D. (1987). Learning regular sets from queries and counterexamples. Inform. Comput., 75:2, 87–106.Google Scholar
  3. Biermann, A.W.,& Feldman, J. A. (1972). On the synthesis of finite-state machines from samples of their behavior. IEEE Transactions on Computers, 21, 592–597.Google Scholar
  4. Biermann, A. W.,& Petry, F. E. (1975). Speeding up the synthesis of programs from traces. IEEE Trans. on Computers, C-24, 122–136.Google Scholar
  5. Blumer, A., Ehrenfeucht, A., Haussler, D.,& Warmuth, M. K. (1986). Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension. In Proc. 19th Annu. ACM Sympos. Theory Comput. (pp. 273–282).Google Scholar
  6. Blumer, A., Ehrenfeucht, A., Haussler, D.,& Warmuth, M. K. (1987). Occam's razor. Inform. Proc. Lett., 24, 377–380.Google Scholar
  7. Bryant, R. E. (1986). Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers, 35, 677–691.Google Scholar
  8. Carraghan, R.,& Pardalos, P. M. (1990). An exact algorithm for the maximum clique problem. Operations Research Letters, 9, 375–382.Google Scholar
  9. Coste, F.,& Nicolas, J. (1998). How considering incompatible state mergings may reduce the DFA induction search tree. In Fourth International Colloquium on Grammatical Inference (ICGI-98) (pp. 199–210). volume. 1433 of Lecture Notes in Computer Science.Google Scholar
  10. Coudert, O., Berthet, C.,& Madre, J. C. (1989).Verification of synchronous sequential machines based on symbolic execution. In Sifakis, J., (Ed.), Proceedings of the Workshop on Automatic Verification Methods for Finite State Systems (pp. 365–373). Springer-Verlag, volume 407 of Lecture Notes in Computer Science.Google Scholar
  11. Davis, M.,& Putnam, H. (1960). A computing procedure for quantification theory. Journal of the Association for Computing Machinery, 7:3, 201–215.Google Scholar
  12. de Kleer, J. (1986). An assumption-based TMS. Artificial Intelligence, 28:2, 127–162.Google Scholar
  13. Garey, M.,& Johnson, D. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York.Google Scholar
  14. Giles, C. L., Miller, C. B., Chen, D., Chen, H. H., Sun, G. Z.,& Lee, Y. C. (1992). Learning and extracting finite state automata with second-order recurrent neural networks. Neural Computation, 4, 393–405.Google Scholar
  15. Gold, E. M. (1972). System identification via state characterization. Automatica, 8, 621–636.Google Scholar
  16. Gold, E. M. (1978). Complexity of automaton identification from given data. Inform. Control, 37, 302–320.Google Scholar
  17. Horne, B. G.,& Giles, C. L. (1995). Advances in Neural Information Processing Systems (Vol. 7) (pp. 697–704). MIT Press.Google Scholar
  18. Juillé, H.,& Pollack, J. B. (1998). A stochastic search approach for grammar induction. In Proceedings of the 1998 International Colloquium on Grammatical Inference (ICGI-98) (pp. 126–137). Lecture Notes in Computer Science.Google Scholar
  19. Kam, T.,& Brayton, R. K. (1990). Multi-valued decision diagrams. Tech. Report No. UCB/ERL M90/125.Google Scholar
  20. Kam, T., Villa, T., Brayton, R.,& Sangiovanni-Vincentelli, A. (1994). A fully implicit algorithm for exact state minimization. In Proc. of the ACM/IEEE Design Automation Conference (pp. 684–690). ACM Press.Google Scholar
  21. Kunz, M. H.,& Pradhan, D. K. (1992). Recursive learning: an attractive alternative to the decision tree for test generation in digital circuits. In Proceedings of the International Test Conference (pp. 816–825).Google Scholar
  22. Lang, K. J. (1992). Random DFA's can be approximately learned from sparse uniform examples. In Proc. 5th Annu. Workshop on Comput. Learning Theory (pp. 45–52). New York, NY: ACM Press.Google Scholar
  23. Lang, K. J., Pearlmutter, B. A.,& Price, R. (1998). Results of the Abbadingo One DFA learning competition and a new evidence driven state merging algorithm. In Fourth International Colloquium on Grammatical Inference (ICGI-98) (pp. 1–12). volume 1433 of Lecture Notes in Computer Science.Google Scholar
  24. Li, M.,& Vitányi, P. M. B. (1994). An Introduction to Kolmogorov Complexity. Addison-Wesley, MA.Google Scholar
  25. Oliveira, A. L., Carloni, L., Villa, T., and Vincentelli, A. S. (1998). Exact minimization of binary decision diagrams using implicit techniques. IEEE Transactions on Computers, 47:11, 1282–1296.Google Scholar
  26. Oliveira, A. L.,& Edwards, S. (1996). Limits of exact algorithms for inference of minimum size finite state machines. In Proceedings of the Seventh Workshop on Algorithmic Learning Theory (pp. 59–66). Sydney, Australia: Springer-Verlag. number 1160 in Lecture Notes in Artificial Intelligence.Google Scholar
  27. Oliveira, A. L.,& Silva, J. P. M. (1998). Efficient search techniques for the inference of minimum size finite automata. In Proceedings of the Fifth String Processing and Information Retrieval Symposium (pp. 81–89). IEEE Computer Press.Google Scholar
  28. Oncina, J.,& Garcia, P. (1992). Inferring regular languages in polynomial update time. In Pattern recognition and image analysis (pp. 49–61). World Scientific.Google Scholar
  29. Pearl, J. (1978). On the connection between the complexity and credibility of inferred models. Journal of General Systems, 4, 255–264.Google Scholar
  30. Pena, J. G.,& Oliveira, A. L. (1998). A new algorithm for the reduction of incompletely specified finite state machines. In Proc. of the ACM/IEEE International Conference on Computer Aided Design (pp. 482–489), San Jose: IEEE Computer Society Press.Google Scholar
  31. Pfleeger, C. F. (1973). State reduction in incompletely specified finite state machines. IEEE Trans. Computers, C-22, 1099–1102.Google Scholar
  32. Pitt, L.,& Warmuth, M. (1993). The minimum consistent DFA problem cannot be approximated within any polynomial. J. ACM, 40:1, 95–142.Google Scholar
  33. Pollack, J. B. (1991). The induction of dynamical recognizers. Machine Learning, 7, 123–148.Google Scholar
  34. Porat, S.,& Feldman, J. A. (1988). Learning automata from ordered examples. In Proc. 1st Annu. Workshop on Comput. Learning Theory (pp. 386–396). San Mateo, CA: Morgan Kaufmann.Google Scholar
  35. Russel, S.,& Norvig, P. (1996). Artificial Intelligence: A Modern Approach. Prentice-Hall.Google Scholar
  36. Schapire, R. E. (1992). The Design and Analysis of Efficient Learning Algorithms. Cambridge, MA: MIT Press.Google Scholar
  37. Silva, J. P. M. (1995). Search Algorithms for Satisfiability Problems in Combinational Switching Circuits. PhD thesis, University of Michigan.Google Scholar
  38. Silva, J. P. M.,& Sakallah, K. (1996).GRASP—A new search algorithm for satisfiability. In Proc. of the ACM/IEEE International Conference on Computer Aided Design (pp. 220–227). IEEE Computer Society Press.Google Scholar
  39. Stallman, R. M.,& Sussman, G. J. (1977). Forward reasoning and dependency-directed backtracking in a system for computer-aided circuit analysis. Artificial Intelligence, 9, 135–196.Google Scholar
  40. Trakhtenbrot, B. A.,& Barzdin, Y. M. (1973). Finite Automata. Amsterdam: North-Holland.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Arlindo L. Oliveira
    • 1
  • João P.M. Silva
    • 1
  1. 1.IST-INESC/Cadence European LabsLisboaPortugal

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