论文标题
并发系统和某些概率应用的光谱属性
A spectral property for concurrent systems and some probabilistic applications
论文作者
论文摘要
我们研究跟踪理论并发系统。此设置包括安全的（1结合）培养皿网。我们引入了不可还原并发系统的概念，并证明了不可还原性和“光谱属性”之间的等效性。光谱特性指出了与系统相关的某些生长序列的收敛性半径之间的严格不平等。我们提供的证据依赖于分析组合技术。光谱特性是我们理论的基石，在一个框架中，Perron-Frobenius理论不直接适用。该限制是并发系统研究中的固有困难。 我们将光谱特性应用于并发系统的概率理论。一方面，我们证明了统一度量的独特性，这是先前论文中的问题。另一方面，我们证明，在状态空间上，可以将这种统一的度量视为可以精确表征的状态空间上的马尔可夫链。
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.
