结构线性方程组解的空间困难性
Space Hardness of Solving Structured Linear Systems
摘要：
我们表明，如果无向Laplacian矩阵的概率空间求解器或确定性的近似空间求解器可以扩展到解决稍大的子类的线性系统，那么它们可以用来解决所有的线性系统具有类似的空间复杂度。以前，Kyng和Zhang在时间复杂度设置中使用近似求解器之间的减少证明了类似的结果。我们证明，他们的减少可以实现使用恒定的深度，多项式大小的阈值电路。
英文摘要：
We show that if the probabilistic logarithmic-space solver or the deterministic nearly logarithmic-space solver for undirected Laplacian matrices can be extended to solve slightly larger subclasses of linear systems, then they can be use to solve all linear systems with similar space complexity. Previously Kyng and Zhang proved similar results in the time complexity setting using reductions between approximate solvers. We prove that their reductions can be implemented using constant-depth, polynomial-size threshold circuits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
