Uniform and Bernoulli measures on the boundary of trace monoids

Samy Abbes, Jean Mairesse
2015 Journal of combinatorial theory. Series A  
Trace monoids and heaps of pieces appear in various contexts in combinatorics. They also constitute a model used in computer science to describe the executions of asynchronous systems. The design of a natural probabilistic layer on top of the model has been a long standing challenge. The difficulty comes from the presence of commuting pieces and from the absence of a global clock. In this paper, we introduce and study the class of Bernoulli probability measures that we claim to be the simplest
more » ... dequate probability measures on infinite traces. For this, we strongly rely on the theory of trace combinatorics with the M\"obius polynomial in the key role. These new measures provide a theoretical foundation for the probabilistic study of concurrent systems.
doi:10.1016/j.jcta.2015.05.003 fatcat:nxyckx5rlvdcncnksvz666duuq