论文标题
学会计算对称性
Learning to Count up to Symmetry
论文作者
论文摘要
在本文中，我们发展了如何在薄薄的游戏中计算如何计数的理论，该策略的配置见证了它达到游戏的某种配置。每当人们打算将并发策略与加权关系模型联系起来时，这在并发游戏的许多最新发展中都起着核心作用。当然，困难是对称性的：在对称性的情况下，策略的许多配置在道德上是相同的不同实例，仅在副本索引的不必要选择上有所不同。我们怎么知道要计算哪些？本文的目的是澄清，揭示了许多奇怪的现象和引人入胜的病理例子。为了说明结果，我们表明，只要涉及的策略没有僵局，就保留了简单加权关系模型的崩溃操作，简单地计算出证人就可以保留在构图下。
In this paper we develop the theory of how to count, in thin concurrent games, the configurations of a strategy witnessing that it reaches a certain configuration of the game. This plays a central role in many recent developments in concurrent games, whenever one aims to relate concurrent strategies with weighted relational models. The difficulty, of course, is symmetry: in the presence of symmetry many configurations of the strategy are, morally, different instances of the same, only differing on the inessential choice of copy indices. How do we know which ones to count? The purpose of the paper is to clarify that, uncovering many strange phenomena and fascinating pathological examples along the way. To illustrate the results, we show that a collapse operation to a simple weighted relational model simply counting witnesses is preserved under composition, provided the strategies involved do not deadlock.
