学习计数到对称

摘要：

在本文中，我们开发的理论，如何计数，在薄并发游戏，配置的策略，见证它达到一定的配置的游戏。这在并发博弈的许多最新发展中起着核心作用，每当一个人的目标是将并发策略与加权关系模型联系起来时。当然，困难在于对称性：在对称性存在的情况下，策略的许多配置在道德上是相同的不同实例，只是在复制索引的非本质选择上有所不同。我们怎么知道该算哪一个？本文的目的是澄清这一点，揭示许多奇怪的现象和迷人的病理学例子。为了说明结果，我们表明，一个简单的加权关系模型简单计数证人的崩溃操作下的组合，提供的策略不死锁。

英文摘要：

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.

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。