TP完备化问题的原子观点
An Atomic Viewpoint of the TP Completion Problem
摘要：
我们提出了两个互补的技术，称为催化和抑制，允许一个确定一个给定的模式是TP可完成或TP不可完成，分别。从经验上讲，这些技术在绝大多数情况下一次只需要考虑一个未指定的条目，这使得这些技术自动化的成熟和一个强大的框架，为未来的工作在TP完成问题。通过小的修改，这些技术也适用于TN完成问题。我们提供两个主要应用。首先，我们用可完成性来刻画所有4 × 4模式。总共有78个这种尺寸的新阻塞，是所有$n$组合的3 × $n$病例的6倍。其次，我们提供了一个表征的TN情况下，其中包括作为一个推论的表征模式与一个单一的未指定的条目，所谓的1-变量障碍。这也提供了一个新的部分结果证明猜想，所有TN-可完成的模式是TP-可完成的。
英文摘要：
We present two complementary techniques called catalysis and inhibition which allow one to determine if a given pattern is TP completable or TP non-completable, respectively. Empirically, these techniques require considering only one unspecified entry at a time in a vast majority of cases, which makes these techniques ripe for automation and a powerful framework for future work in the TP completion problem. With small modifications, these techniques are also applicable to the TN completion problem. We provide two major applications. First, we characterize all 4-by-4 patterns by completability. There are a total of 78 new obstructions of this size, six times as many as the 3-by-$n$ case for all $n$ combined. Second, we provide a characterization of the so-called 1-variable obstructions in the TN case, which includes as a corollary a characterization of patterns with a single unspecified entry. This also provides a novel partial result towards proving the conjecture that all TN-completable patterns are TP-completable.
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。
