Extracting string motif bases for quorum higher than two

Bases of generators of motifs consisting of strings in which some positions can be occupied by a don’t care provide a useful conceptual tool for their description and a way to reduce the time and space involved in the discovery process. In the last few years, a few algorithms have been proposed for the extraction of a basis, building in large part on combinatorial properties of strings and their autocorrelations. Currently, the most efficient techniques for binary alphabets and quorum q = 2 require time quadratic in the length of the host string. The present paper explores properties of motif bases for quorum q ≥ 2, both with binary and general alphabets, by also showing that important results holding for quorum q = 2 cannot be extended to this, more general, case. Furthermore, the extraction of motifs in which a bound is set on the maximum allowed number of don’t cares is addressed, and suitable algorithms are proposed whose computational complexity depends on the fixed bound.