Longest Motifs with a Functionally Equivalent Central Block

This paper presents a generalization of the notion of longest repeats with a block of k don’t care symbols introduced by [8] (for k fixed) to longest motifs composed of three parts: a first and last that parameterize match (that is, match via some symbol renaming, initially unknown), and a functionally equivalent central block. Such three-part motifs are called longest block motifs. Different types of functional equivalence, and thus of matching criteria for the central block are considered, which include as a subcase the one treated in [8] and extend to the case of regular expressions with no Kleene closure or complement operation. We show that a single general algorithmic tool that is a non-trivial extension of the ideas introduced in [8] can handle all the various kinds of longest block motifs defined in this paper. The algorithm complexity is, in all cases, in O(n log n).