Year: 2026
Type: preprint
Abstract: We consider systems of submatrix equations, that is, sets of equality constraints over square submatrices of the input. By generalising the recursive algorithm of Gawrychowski et al. [Universal reconstruction of a string, Theoretical Computer Science 2020] to two dimensions, we obtain a linear-time procedure that finds a solution for any such input system. As an immediate by-product, this yields an optimal-time algorithm for decompressing any two-dimensional macro scheme based on copy operations of sub-squares.
Source: arXiv (Cornell University)
Authors: Carfagna, Lorenzo, Manzini, Giovanni
Institution: University of Pisa
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203485647
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