Discovering unbounded unions of regular pattern languages from positive examples

Abstract

The problem of learning unions of certain pattern languages from positive examples is considered. We restrict to the regular patterns, i.e., patterns where each variable symbol can appear only once, and to the substring patterns, which is a subclass of regular patterns of the type xαy, where x and y are variables and α is a string of constant symbols. We present an algorithm that, given a set of strings, finds a good collection of patterns covering this set. The notion of a ‘good covering’ is defined as the most probable collection of patterns likely to be present in the examples, assuming a simple probabilistic model, or equivalently using the Minimum Description Length (MDL) principle. Our algorithm is shown to approximate the optimal cover within a logarithmic factor. This extends a similar recent result for the so-called simple patterns. For substring patterns the running time of the algorithm is O(nN), where n is the number and N the total lenght of the sequences.