Polynomial time inference of general pattern languages

Abstract

Assume a finite alphabet of constant symbols and a disjoint infinite alphabet of variable symbols. A pattern p is a non-empty string of constant and variable symbols. The language L(p) is the set of all words over the alphabet of constant symbols generated from p by substituting some non-empty words for the variables in p. A sample S is a finite set of words over the same alphabet. A pattern p is descriptive of a sample S if and only if it is possible to generate all elements of S from p and, moreover, there is no other pattern q also able to generate S such that L(q) is a proper subset of L(p). The problem of finding a pattern being descriptive of a given sample is studied. It is known that the problem of finding a pattern of maximal length is NP-hard. Till now has be known a polynomial-time algorithm only for the special case of patterns containing only one variable symbol. The main result is a polynomial time algorithm constructing descriptive patterns of maximal length for the general case of patterns containing variable symbols from any finite set a priori fixed.KeywordsInductive InferenceConstant SymbolInput WordPattern LanguageVariable SymbolThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.