Polynomial-time inference of arbitrary pattern languages

Abstract

A pattern is a finite string of constants and variables (cf. [1]). The language of a pattern is the set of all strings which can be obtained by substituting non-null strings of constants for the variables of the pattern. In the present paper, we consider the problem of learning pattern languages from examples. As a main result we present an inconsistent polynomial-time algorithm which identifies every pattern language in the limit. Furthermore, we investigate inference of arbitrary pattern languages within the framework of learning from good examples. Finally, we show that every pattern language can be identified in polynomial time from polynomially many disjointness queries, only.