Solving Square-Submatrix Equation Systems

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.

11 pages, 3 figures