Synchronization of Bernoulli sequences on shared letters

TL;DR

This paper investigates the probabilistic synchronization of Bernoulli sequences on shared alphabets, introducing algorithms for generating random traces in concurrent systems, with applications to path and ring models.

Contribution

It introduces two local-random-primitive algorithms for generating Bernoulli-distributed traces in shared-letter sequences, advancing probabilistic modeling of concurrent systems.

Findings

Algorithms successfully generate Bernoulli-distributed traces.

Applicable to path and ring models of arbitrary size.

Includes uniform trace generation as a special case.

Abstract

The topic of this paper is the distributed and incremental generation of long executions of concurrent systems, uniformly or more generally with weights associated to elementary actions. Synchronizing sequences of letters on alphabets sharing letters are known to produce a trace in the concurrency theoretic sense, i.e., a labeled partially ordered set. We study the probabilistic aspects by considering the synchronization of Bernoulli sequences of letters, under the light of Bernoulli and uniform measures recently introduced for trace monoids. We introduce two algorithms that produce random traces, using only local random primitives. We thoroughly study some specific examples, the path model and the ring model, both of arbitrary size. For these models, we show how to generate any Bernoulli distributed random traces, which includes the case of uniform generation.