二维的Sperner/Brouwer函数路径跟踪解的复杂性
The Complexity of the Path-following Solutions of Two-dimensional Sperner/Brouwer Functions
摘要：
有许多结果表明，对于某些解决PPAD完全问题的“路径跟踪”算法，该算法获得的解是PSPACE完全计算的。我们猜想，这些结果是一个更一般的原则，所有这些算法计算PSPACE完全解决方案的特殊情况。这样一个一般性的结果可能为复杂性类PPAD提供新的线索。在本文中，我们提出了一个新的PSPACE-完备性结果的一个有趣的挑战的情况下，这个猜想。Chen和Deng~ \cite{CD}证明了在简洁表示的Sperner三角剖分中寻找三色三角形是PPAD完全的。Sperner引理的证明--这样的解总是存在的--特别指出了一个解，它是通过自然的“路径跟踪”方法找到的。在这里，我们表明，它是PSPACE-完全的计算这个特定的解决方案，连同一个类似的结果计算的路径跟踪解决方案的二维的【形】离散布劳威尔函数。
英文摘要：
There are a number of results saying that for certain "path-following" algorithms that solve PPAD-complete problems, the solution obtained by the algorithm is PSPACE-complete to compute. We conjecture that these results are special cases of a much more general principle, that all such algorithms compute PSPACE-complete solutions. Such a general result might shed new light on the complexity class PPAD. In this paper we present a new PSPACE-completeness result for an interesting challenge instance for this conjecture. Chen and Deng~\cite{CD} showed that it is PPAD-complete to find a trichromatic triangle in a concisely-represented Sperner triangulation. The proof of Sperner's lemma --- that such a solution always exists --- identifies one solution in particular, that is found via a natural "path-following" approach. Here we show that it is PSPACE-complete to compute this specific solution, together with a similar result for the computation of the path-following solution of two-dimensional discrete Brouwer functions.
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。
