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Uniform and Bernoulli measures on the boundary of trace monoids

By Samy Abbes and Jean Mairesse


International audienceTrace 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 adequate probability measures on infinite traces. For this, we strongly rely on the theory of trace combinatorics with the Möbius polynomial in the key role. These new measures provide a theoretical foundation for the probabilistic study of concurrent systems

Topics: Trace monoid, Uniform measure, Random heaps, Möbius polynomial, [ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO]
Publisher: Elsevier
Year: 2015
DOI identifier: 10.1016/j.jcta.2015.05.003
OAI identifier: oai:HAL:hal-01158021v1
Provided by: Hal-Diderot
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