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Learning two-tape automata from queries and counterexamples

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Abstract

We investigate the learning problem of two-tape deterministic finite automata (2-tape DFAs) from queries and counterexamples. Instead of accepting a subset of ∑*, a 2-tape DFA over an alphabet ∑ accepts a subset of ∑* × ∑*, and therefore, it can specify a binary relation on ∑*. In [3] Angluin showed that the class of deterministic finite automata (DFAs) is learnable in polynomial time from membership queries and equivalence queries, namely, from a minimally adequate teacher (MAT).

In this article we show that the class of 2-tape DFAs is learnable in polynomial time from MAT. More specifically, we show an algorithm that, given any languageL accepted by an unknown 2-tape DFAM, learns from MAT a two-tape nonde-terministic finite automaton (2-tape NFA)M′ acceptingL in time polynomial inn andl, wheren is the size ofM andl is the maximum length of any counterexample provided during the learning process.

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Authors and Affiliations

  1. Department of Computer Science and Information Mathematics, University of Electro-Communications, 1-5-1 Choufugaoka, Chofu, 182, Tokyo, Japan

    T. Yokomori

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  1. T. Yokomori
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This work was supported in part by Grants-in-Aid for Scientific Research No. 04229105 from the Ministry of Education, Science, and Culture, Japan.

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Yokomori, T. Learning two-tape automata from queries and counterexamples. Math. Systems Theory 29, 259–270 (1996). https://doi.org/10.1007/BF01201279

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  • DOI: https://doi.org/10.1007/BF01201279

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