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arXiv · 2608.13408

Solving Square-Submatrix Equation Systems

Lorenzo Carfagna·Giovanni Manzini
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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.

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Lorenzo Carfagna, Giovanni Manzini. 2026-08-13. Solving Square-Submatrix Equation Systems. https://arxiv.org/abs/2608.13408

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