# Subsequences With Gap Constraints: Complexity Bounds for Matching and Analysis Problems

arXiv: https://arxiv.org/abs/2206.13896 · HTML: https://mlsanity.com/paper/2206.13896/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2022.

## Built on by (most cited first, 1 of 1)

- [Directed Regular and Context-Free Languages](https://mlsanity.com/paper/2401.07106/) (2024)

## Abstract (arXiv)

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, ..., Ck-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) ∈ mathbbN2 and/or regular languages Ci ∈ 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.