2020/06/09 by Pierre Clairambault, Clairambault, Pierre
Computer Science · Mathematics · Social Sciences · #Computational Physics and Python Applications #FOS: Computer and information sciences #History and Theory of Mathematics #Logic in Computer Science (cs.LO) #Programming Languages (cs.PL) #Science Education and Pedagogy
paper · doi:10.48550/arxiv.2006.05080
openalex publication_date 2020/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.