Subsequences With Gap Constraints: Complexity Bounds for Matching and Analysis Problems
(2206.13896)Abstract
We consider subsequences with gap constraints, i.e., length-k subsequences p that can be embedded into a string w such that the induced gaps (i.e., the factors of w between the positions to which p is mapped to) satisfy given gap constraints $gc = (C1, C2, ..., C{k-1})$; we call p a gc-subsequence of w. In the case where the gap constraints gc are defined by lower and upper length bounds $Ci = (L-_i, L+_i) \in \mathbb{N}2$ and/or regular languages $C_i \in REG$, we prove tight (conditional on the orthogonal vectors (OV) hypothesis) complexity bounds for checking whether a given p is a gc-subsequence of a string w. We also consider the whole set of all gc-subsequences of a string, and investigate the complexity of the universality, equivalence and containment problems for these sets of gc-subsequences.
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