Abstract
This paper surveys recent results concerning the inference of deterministic finite automata (DFAs). The results discussed determine the extent to which DFAs can be feasibly inferred, and highlight a number of interesting approaches in computational learning theory.
Supported in part by NSF grant IRI-8809570, and by the Department of Computer Science, University of Illinois at Urbana-Champaign.
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References
N. Abe. Polynomial learnability as a formal model of natural language acquisition. 1989. Ph.D. Thesis, in preparation, Department of Computer and Information Science, University of Pennsylvania.
N. Abe. Polynomial learnability of semilinear sets. In Proceedings of the 1989 Workshop on Computational Learning Theory, Morgan Kaufmann, San Mateo, CA, August 1989.
W. Alexi, B. Chor, O. Goldreich, and C. P. Schnorr. RSA and Rabin functions: certain parts are as hard as the whole. S.I.A.M. Journal on Computing, 17(2):194–209, 1988.
D. Angluin. Equivalence queries and approximate fingerprints. In Proceedings of the 1989 Workshop on Computational Learning Theory, Morgan Kaufmann, San Mateo, CA, August 1989.
D. Angluin. Inference of reversible languages. J. ACM, 29(3):741–765, 1982.
D. Angluin. Learning regular sets from queries and counterexamples. Information and Computation, 75(2):87–106, 1987.
D. Angluin. Negative Results for Equivalence Queries. Technical Report YALEU/DCS/RR-648, Department of Computer Science, Yale University, September 1988.
D. Angluin. A note on diversity. December 1987. Unpublished manuscript.
D. Angluin. A note on the number of queries needed to identify regular languages. Information and Computation, 51:76–87, 1981.
D. Angluin. On the complexity of minimum inference of regular sets. Inform. Contr., 39(3):337–350, 1978.
D. Angluin. Queries and concept learning. Machine Learning, 2:319–342, 1987.
D. Angluin and C. H. Smith. Inductive inference: theory and methods. Computing Surveys, 15(3):237–269, 1983.
J. M. Barzdin. Prognostication of automata and functions, pages 81–84. Elsevier North-Holland, New York, 1972.
J. M. Barzdin and R. V. Freivald. On the prediction of general recursive functions. Soviet Mathematics Doklady, 13:1224–1228, 1972.
P. Berman and R. Roos. Learning one-counter languages in polynomial time. In Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Washington, D.C., October 1987.
L. Blum and M. Blum. Toward a mathematical theory of inductive inference. Inform. Contr., 28:125–155, 1975.
A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth. Learnability and the Vapnik-Chervonenkis Dimension. Technical Report UCSC-CRL-87-20, Department of Computer and Information Sciences, University of California, Santa Cruz, November 1987. To appear, J. ACM.
A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth. Occam's razor. Inform. Process. Letters, 24:377–380, 1987.
R. A. Board and L. Pitt. Sufficent conditions for the necessity of Occam algorithms. 1989. Manuscript in preparation.
J. Case and C. Smith. Comparison of identification criteria for machine inductive inference. Theoretical Computer Science, 25:193–220, 1983.
R. Daley and C. H. Smith. On the complexity of inductive inference. Information and Control, 69:12–40, 1986.
A. Ehrenfeucht, D. Haussler, M. Kearns, and L. G. Valiant. A general lower bound on the number of examples needed for learning. In Proceedings of the 1988 Workshop on Computational Learning Theory, pages 139–154, Morgan Kaufmann, San Mateo, CA, August 1988.
M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman, San Francisco, California, 1979.
J. Gill. Probabilistic Turing machines. SIAM J. Computing, 6(4):675–695, 1977.
E. M. Gold. Complexity of automaton identification from given data. Inform. Contr., 37:302–320, 1978.
E. M. Gold. Language identification in the limit. Inform. Contr., 10:447–474, 1967.
E. M. Gold. System identification via state characterization. Automatica, 8:621–636, 1972.
D. Haussler. Learning Conjunctive Concepts in Structural Domains. Technical Report UCSC-CRL-87-01, Department of Computer and Information Sciences, University of California, Santa Cruz, February 1987. To appear in Machine Learning.
D. Haussler, M. Kearns, N. Littlestone, and M. K. Warmuth. Equivalence of models for polynomial learnability. In Proceedings of the 1988 Workshop on Computational Learning Theory, pages 42–55, Morgan Kaufmann, San Mateo, CA, August 1988.
D. Helmbold, R. Sloan, and M. K. Warmuth. Learning Submodules and Reversible Commutative Regular Languages. 1989. Technical report to appear; Department of Computer and Information Sciences, University of California at Santa Cruz.
D. Helmbold, R. Sloan, and M. K. Warmuth. Learning nested differences of intersection closed concept classes. In Proceedings of the 1989 Workshop on Computational Learning Theory, Morgan Kaufmann, San Mateo, CA, August 1989.
J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, Massachussetts, 1979.
O. H. Ibarra and T. Jiang. Learning regular languages from counterexamples. In Proceedings of the 1988 Workshop on Computational Learning Theory, pages 371–385, Morgan Kaufmann, San Mateo, CA, August 1988.
M. Kearns and L. G. Valiant. Cryptographic limitations on learning Boolean formulae and finite automata. In Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pages 433–444, Assoc. Comp. Mach., New York, May 1989.
M. Li and U. Vazirani. On the learnability of finite automata. In Proceedings of the 1988 Workshop on Computational Learning Theory, pages 359–370, Morgan Kaufmann, San Mateo, California, August 1988.
M. Li and P. Vitanyi. Inductive reasoning and Kolmogorov complexity. In Proceedings of the 4rd Annual IEEE Conference on Structure in Complexity Theory, IEEE Computer Society Press, Washington, D.C., June 1989.
N. Littlestone. Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm. Machine Learning, 2:285–318, 1987.
E. F. Moore. Gedanken-experiments on sequential machines, pages 129–153. Princeton University Press, Princeton, NJ, 1956.
I. Niven and H. S. Zuckerman. An Introduction to the Theory of Numbers. John Wiley and Sons, Inc., New York, 1972.
William of Occam. “Entities should not be multiplied unnecessarily”. c. 1320. Comment regarding superfluous elaboration.
L. Pitt and L. G. Valiant. Computational limitations on learning from examples. J. ACM, 35(4):965–984, 1988.
L. Pitt and M. K. Warmuth. The Minimum Consistent DFA Problem Cannot be Approximated within any Polynomial. Technical Report UIUCDCS-R-89-1499, University of Illinois at Urbana-Champaign, February 1989. A preliminary version appears in the 21st annual ACM Symposium on Theory of Computing, May, 1989.
L. Pitt and M. K. Warmuth. Prediction Preserving Reducibility. Technical Report UCSC-CRL-88-26, University of California, Santa Cruz, November 1988. Preliminary version appeared in Proceedings of the 3rd Annual IEEE Conference on Structure in Complexity Theory, pp. 60–69, June, 1988.
K. M. Podnieks. Comparing various concepts of function prediction, part 1. Latv. Gosudarst. Univ Uch. Zapiski, 210:68–81, 1974. (in Russian).
K. M. Podnieks. Comparing various concepts of function prediction, part 2. Latv. Gosudarst. Univ Uch. Zapiski, 233:33–44, 1975. (in Russian).
S. Porat and J. A. Feldman. Learning automata from ordered examples. In Proceedings of the 1988 Workshop on Computational Learning Theory, pages 386–396, Morgan Kaufmann, San Mateo, CA, August 1988.
M. O. Rabin. Digital Signatures and Public Key Functions as Intractable as Factoring. Technical Report TM-212, Laboratory for Computer Science, M.I.T., 1979.
J. Rissanen. Minimum Description Length Principle, pages 523–527. Wiley, New York, 1985.
R. L. Rivest. Learning decision lists. Machine Learning, 2:229–246, 1987.
R. L. Rivest and R. E. Schapire. Diversity-based inference of finite automata. In Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science, pages 296–304, IEEE Computer Society Press, Washington, D.C., October 1987.
R. L. Rivest and R. E. Schapire. Inference of finite automata using homing sequences. In Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pages 411–420, Assoc. Comp. Mach., New York, 1989.
R. L. Rivest and R. E. Schapire. Inference of visible simple assignment automata with planned experiments. October 1987. Unpublished manuscript, MIT Lab. for Computer Science, Cambridge, MA 02139.
R. L. Rivest, A. Shamir, and L. Adleman. A method for obtaining digital signatures and public key cryptosytems. Communications of the A.C.M., 21(2):120–126, 1978.
Y. Sakakibara. Learning context-free grammars from structural data in polynomial time. In Proceedings of the 1988 Workshop on Computational Learning Theory, pages 330–344, Morgan Kaufmann, San Mateo, CA, August 1988.
R. Schapire. The strength of weak learnability. In Proceedings of the 1989 Workshop on Computational Learning Theory, Morgan Kaufmann, San Mateo, CA, August 1989.
R. Solomonoff. A formal theory of inductive inference, parts 1 and 2. Information and Control, 7:1–22 and 224–254, 1964.
B. A. Trakhtenbrot and Ya. M. Barzdin. Finite Automata. North-Holland, Amsterdam, 1973. pp. 98–99.
L. G. Valiant. A theory of the learnable. Comm. Assoc. Comp. Mach., 27(11):1134–1142, 1984.
C. K. Yap. Theory of Complexity Classes. Oxford University Press, Oxford. To appear.
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Pitt, L. (1989). Inductive inference, DFAs, and computational complexity. In: Jantke, K.P. (eds) Analogical and Inductive Inference. AII 1989. Lecture Notes in Computer Science, vol 397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51734-0_50
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DOI: https://doi.org/10.1007/3-540-51734-0_50
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