Regular Expression Constrained Sequence Alignment

Given strings S1, S2, and a regular expression R, we introduce regular expression constrained sequence alignment as the problem of finding the maximum alignment score between S1 and S2 over all alignments such that in these alignments there exists a segment where some substring s1 of S1 is aligned with some substring s2 of S2, and both s1 and s2 match R, i.e. s1, s2 ∈ L(R) where L(R) is the regular language described by R. A motivation for the problem is that protein sequences can be aligned in a way that known motifs guide the alignments. We present an O(nmr) time algorithm for the regular expression constrained sequence alignment problem where n, and m are the lengths of S1, and S2, respectively, and r is in the order of the size of the transition function of a finite automaton M that we create from a nondeterministic finite automaton N accepting L(R). M contains O(t) states if N has t states.