Traces via Strategies in Two-Player Games
Abstract
Traces form a coarse notion of semantic equivalence between states of a process, and have been studied coalgebraically for various types of system. We instantiate the finitary coalgebraic trace semantics framework of Hasuo et al. for controller-versus-environment games, encompassing both nondeterministic and probabilistic environments. Although our choice of monads is guided by the constraints of this abstract framework, they enable us to recover familiar game-theoretic concepts. Concretely, we show that in these games, each element in the trace map corresponds to a collection (a subset or distribution) of plays the controller can force. Furthermore, each element can be seen as the outcome of following a controller strategy. Our results are parametrised by a weak distributive law, which computes what the controller can force in a single step.
Cite
@article{arxiv.2510.24252,
title = {Traces via Strategies in Two-Player Games},
author = {Benjamin Plummer and Corina Cirstea},
journal= {arXiv preprint arXiv:2510.24252},
year = {2026}
}