分布式综合的一个收缩定理
A Retraction Theorem for Distributed Synthesis
摘要：
我们提出了一个一般性定理的分布式综合问题的协调对策与$ω$ -定期目标的形式：如果存在一个获胜的战略联盟，那么存在一个“本质”的获胜策略，这是通过收回给定的。一般来说，这不会导致有限状态获胜策略，但当代理的知识保持有界时，我们可以解决综合问题。我们的研究是在这样的环境中进行的，其中目标是以可能观察到\emph{not}的事件来表达的。这在不完全信息的博弈中是很自然的，而不是通常的假设，即目标是用所有主体都能观察到的事件来表达的。利用知识状态的有限性和由知识状态导出的有限同余类，研究了可判定的分布式综合问题。
英文摘要：
We present a general theorem for distributed synthesis problems in coordination games with $ω$-regular objectives of the form: If there exists a winning strategy for the coalition, then there exists an "essential" winning strategy, that is obtained by a retraction of the given one. In general, this does not lead to finite-state winning strategies, but when the knowledge of agents remains bounded, we can solve the synthesis problem. Our study is carried out in a setting where objectives are expressed in terms of events that may \emph{not} be observable. This is natural in games of imperfect information, rather than the common assumption that objectives are expressed in terms of events that are observable to all agents. We characterise decidable distributed synthesis problems in terms of finiteness of knowledge states and finite congruence classes induced by them.
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