Abstract
We show that the class of languages generated by (basic) recurrence-terms is inferable in the limit from positive data, and that such learning may be consistent and conservative, though not in general strong monotonic. This class of languages has neither of the properties of finite thickness and finite elasticity usually used to prove inferability from positive data, so our proof method is the explicit construction of a tell-tale function for the class of recurrence-term languages. Recurrence-terms are of interest because they generate many sequences arising from divergent cases of Knuth-Bendix completion.
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References
D. Angluin, Inductive inference of formal languages from positive data, Information and Control 45, 117–135, 1980.
D. Angluin, C.H. Smith, Inductive inference: theory and methods, Computing Surveys 15, 237–269, 1983.
H. Chen, J. Hsiang, H.-C. Kong, On finite representations of infinite sets of terms, in Proc. of the Second International Workshop on Typed and Conditional Rewrite Systems, Montreal 1990, Lecture Notes in Computer Science 516, 100–114, Springer-Verlag, 1990.
N. Dershowitz, Synthesis by completion, in Proc. 9th International Joint Conference on Artificial Intelligence, Los Angeles, CA, 1985.
N. Dershowitz, E. Pinchover, Inductive synthesis of equational programs, in Proc. of AIII-90, 1990.
E.M. Gold, Language identification in the limit, Information and Control 10, 447–474, 1967.
International Organisation for Standardisation, Information processing systems — open systems interconnection — LOTOS — a formal description technique based on the temporal ordering of observational behaviour, 1988.
K.P. Jantke, Monotonic and non-monotonic inductive inference, New Generation Computing 8, 349–360.
D. Knuth, P. Bendix, Simple word problems in universal algebra, in J. Leech (Ed.), Computational Problems in Abstract Algebra, Pergamon Press, 1970.
St. Lange, Towards a set of inference rules for solving divergence in Knuth-Bendix completion, in K.P. Jantke (Ed.), Proc. Analogical and Inductive Inference '89, GDR, Lecture Notes in Computer Science 397, 304–316, Springer-Verlag, 1989.
St. Lange, T. Zeugmann, Monotonic versus non-monotonic language learning, in G. Brewka, K.P. Jantke and P. H. Schmitt (Eds.), Proc. Second International Workshop on Nonmonotonic and Inductive Logics, Reinhardsbrunn 1991, Lecture Notes in Artificial Intelligence, 659, 254–269, Springer-Verlag, 1993.
T. Motoki, T. Shinohara, Correct definition of finite elasticity, Technical Report RIFIS-TR-CS-29, Kyushu University, 1990.
T. Shinohara, Polynomial time inference of extended regular pattern languages, in Proc. RIMS Symposia on Software Science and Engineering, Kyoto, 1982, Lecture Notes in Computer Science 147, 115–127, Springer-Verlag, 1982.
T. Shinohara, Inductive inference of monotonic formal systems from positive data, New Generation Computing 8, 371–384, 1991.
M. Thomas, K.P. Jantke, Inductive inference for solving divergence in Knuth-Bendix completion, in K.P. Jantke (Ed.), Proc. Analogical and Inductive Inference '89, GDR, Lecture Notes in Computer Science 397, 288–303, Springer-Verlag, 1989.
M. Thomas, P. Watson, Solving divergence in Knuth-Bendix completion by enriching signatures, Theoretical Computer Science 112, 145–185, 1993.
P. Watson, The expressive power of recurrence-terms, University of Glasgow, Department of Computing Science technical report FM 92-6, 1992.
P.Watson, Inductive learning of extended pattern languages from text, to appear.
R. Wiehagen, A Thesis in inductive inference, in J. Dix, K.P. Jantke and P.H. Schmitt (Eds.), Proc. First International Workshop on Nonmonotonic and Inductive Logics, Karlsruhe 1990, Lecture Notes in Artificial Intelligence, 543, 184–207, Springer-Verlag, 1991.
K. Wright, Identification of unions of languages drawn from an identifiable class, Proc. 2nd Workshop Comput. Learning Theory, 328–333, 1989.
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© 1995 Springer-Verlag Berlin Heidelberg
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Watson, P. (1995). Inductive learning of recurrence-term languages from positive data. In: Jantke, K.P., Lange, S. (eds) Algorithmic Learning for Knowledge-Based Systems. Lecture Notes in Computer Science, vol 961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60217-8_14
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DOI: https://doi.org/10.1007/3-540-60217-8_14
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