Abstract
When concerned about efficient grammatical inference two issues are relevant: the first one is to determine the quality of the result, and the second is to try to use polynomial time and space. A typical idea to deal with the first point is to say that an algorithm performs well if it identifies in the limit the correct language. The second point has led to debate about how to define polynomial time: the main definitions of polynomial inference have been proposed by Pitt and Angluin. We return in this paper to another definition proposed by Gold that requires a characteristic set of strings to exist for each grammar, and this set to be polynomial in the size of the grammar or automaton that is to be learnt, where the size of the sample is the sum of the lengths of all its words. The learning algorithm must also infer correctly as soon as the characteristic set is included in the data. We first show that this definition corresponds to a notion of teachability as defined by Goldman and Mathias. By adapting their teacher/learner model to grammatical Inference we prove that languages given by context-free grammars, simple deterministic grammars, linear grammars and nondeterministic finite automata are not polynomially identifiable from given data.
This work has been performed while the author was visiting the Universidad Politecnica de Valencia, Spain.
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Bibliography
Angluin, D. (1987). Queries and concept learning. Machine Learning 2, 319–342.
Anthony, M., Brightwell, G., Cohen, D. & Shawe-Taylor, J. (1992). On exact specification by examples. Proceedings of COLT 92 (pp. 311–318). A.C.M.
Castellanos, A., Galiano I. & Vidal, E. (1994). Application of OSTIA to machine translation tasks. Proceedings of the International Colloquium on Grammatical Inference ICGI-94 (pp. 93–105). Lecture Notes in Artificial Intelligence 862, Springer-Verlag.
Freivalds, R., Kinber, E.B. & Wiehagen, R. (1989). Inductive inference from good examples. Proceedings of the International Workshop on Analogical and Inductive Inference (pp. 1–17). Lecture Notes in Artificial Intelligence 397, Springer-Verlag.
García, P., Segarra, E., Vidal, E. & Galiano, I. (1994). On the use of the morphic generator grammatical inference (MGGI) methodology in automatic speech recognition. International Journal of Pattern Recognition and Artificial Intelligence 4, 667–685.
García, P. & Vidal, E. (1990). Inference of K-testable languages in the strict sense and applications to syntactic pattern recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 12 /9, 920–925.
Garey, M.R. & Johnson, D.S. (1979). Computers and intractability: a guide to the theory of NP-completeness. San Francisco: W.H. Freeman.
Gold, E.M. (1967). Language identification in the limit. Inform. & Control. 10, 447–474.
Gold, E.M. (1978). Complexity of automaton identification from given data. Information and Control 37, 302–320.
Goldman, S.A. & Kearns M.J. (1991). On the complexity of teaching. Proceedings of COLT' 91 (pp. 303–314).
Goldman, S.A. & Mathias, H.D. (1993). Teaching a smarter learner. Proceedings of COLT' 93 (pp. 67–76).
Harrison, M.A. (1978). Introduction to formal language theory. Reading: Addison-Wesley.
Ishizaka, I. (1989). Learning simple deterministic languages. Proceedings of COLT' 89 (pp. 162–174). A.C.M.
Jackson, J. & Tomkins, A. (1992). A computational model of teaching. Proceedings of COLT' 92 (pp. 319–326). A.C.M.
Koshiba, T., Mäkinen, E. & Takada, Y. (1995). Learning deterministic even linear languages from positive examples. Proceedings of ALT '95, Lecture Notes in Artificial Intelligence 997, Springer-Verlag.
Oncina, J. & García, P. (1992) Inferring regular languages in polynomial time. In Pattern Recognition and Image Analysis, World Scientific.
Oncina, J., García, P. & Vidal E. (1993). Learning subsequential transducers for pattern recognition tasks. IEEE Transactions on Pattern Analysis and Machine Intelligence 15, 448–458.
Pitt, L. (1989). Inductive inference, dfas and computational complexity. Proceedings of the International Workshop on Analogical and Inductive Inference (pp. 18–44). Lecture Notes in Artificial Intelligence 397, Springer-Verlag.
Sempere, J.M. & García, P. (1994). A characterisation of even linear languages and its application to the learning problem. Proceedings of the International Colloquium on Grammatical Inference ICGI-94 (pp. 38–44). Lecture Notes in Artificial Intelligence 862, Springer-Verlag.
Takada, Y. (1988). Grammatical inference for even linear languages based on control sets. Information Processing Letters 28, 193–199.
Takada, Y. (1994). A hierarchy of language families learnable by regular language learners. Proceedings of the International Colloquium on Grammatical Inference ICGI-94 (pp. 16–24). Lecture Notes in Artificial Intelligence 862, Springer-Verlag.
Wiehagen, R. (1992). From inductive inference to algorithmic learning theory. Proceedings of ALT' 92, (pp 13–24). Lecture Notes in Artificial Intelligence 743, Springer-Verlag.
Yokomori, T. (1993). Learning non-deterministic finite automata from queries and counterexamples. Machine Intelligence 13. Furukawa, Michie & Muggleton eds., Oxford Univ. Press.
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De La Higuera, C. (1996). Characteristic sets for polynomial grammatical inference. In: Miclet, L., de la Higuera, C. (eds) Grammatical Interference: Learning Syntax from Sentences. ICGI 1996. Lecture Notes in Computer Science, vol 1147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033342
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DOI: https://doi.org/10.1007/BFb0033342
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