Subsequences With Gap Constraints: Complexity Bounds for Matching and Analysis Problems
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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 = (C_1, C_2, ..., 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 C_i = (L^-_i, L^+_i) ∈ℕ^2 and/or regular languages C_i ∈ 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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