求解平方子矩阵方程组
Solving Square-Submatrix Equation Systems
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中文总结 AI 辅助
该研究将Gawrychowski等人的字符串重构递归算法推广到二维，得到线性时间求解平方子矩阵方程组的方法，还可用于二维宏方案的最优时间解压。
中文摘要 AI 辅助
我们研究子矩阵方程组，即对输入的平方子矩阵施加的一组等式约束。通过将Gawrychowski等人2020年《Theoretical Computer Science》中提出的字符串通用重构递归算法推广到二维，我们得到了一种线性时间过程，可求解任意此类输入系统。作为直接副产品，该算法能为基于子平方复制操作的任意二维宏方案提供最优时间的解压算法。
英文摘要
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.
