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 reg...

We classify the growth of a k-regular sequence based on information from its k-kernel. In order to provide such a classification, we introduce the notion of a growth exponent for k-regular sequences and show that this exponent is equal to the joint spectral radius of any set of a special class of matrices determined by the k-kernel.