并发系统的谱性质及其概率应用
A spectral property for concurrent systems and some probabilistic applications
摘要：
我们研究迹论并发系统。此设置包含安全（1-有界）Petri网。引入了不可约并发系统的概念，证明了不可约并发系统与谱性质的等价性。谱的性质表明了与系统相关的某些增长级数的收敛半径之间的严格不等式。我们提出的证明依赖于分析组合学技术。谱性质是我们理论的基石，在一个框架中，Perron-Frobenius理论不直接适用。这种限制是并发系统研究中的一个固有困难。我们将谱性质应用于并发系统的概率理论。我们证明一方面的唯一性的统一措施，一个问题在以前的文件中留下的开放。另一方面，我们证明了这种统一的措施，可以实现为一个马尔可夫链的状态和集团的状态空间，可以精确地表征。
英文摘要：
We study trace theoretic concurrent systems. This setting encompasses safe (1-bounded) Petri nets. We introduce a notion of irreducible concurrent system and we prove the equivalence between irreducibility and a "spectral property". The spectral property states a strict inequality between radii of convergence of certain growth series associated with the system. The proof that we present relies on analytic combinatorics techniques. The spectral property is the cornerstone of our theory, in a framework where the Perron-Frobenius theory does not apply directly. This restriction is an inherent difficulty in the study of concurrent systems. We apply the spectral property to the probabilistic theory of concurrent systems. We prove on the one hand the uniqueness of the uniform measure, a question left open in a previous paper. On the other hand, we prove that this uniform measure can be realized as a Markov chain of states-and-cliques on a state space that can be precisely characterized.
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