Polynomial time learnability of simple deterministic languages

Abstract

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This paper is concerned with the problem of learning simple deterministic languages. The algorithm described in this paper is based on the theory of model inference given by Shapiro. In our setting, however, nonterminal membership queries, except for the start symbol, are not permitted. Extended equivalence queries are used instead. Nonterminals that are necessary for a correct grammar and their intended models are introduced automatically. We give an algorithm that, for any simple deterministic languageL, outputs a grammarG in 2-standard form, such thatL=L(G), using membership queries and extended equivalence queries. We also show that the algorithm runs in time polynomial in the length of the longest counterexample and the number of nonterminals in a minimal grammar forL.