相关论文: Deficiency Zero Petri Nets and Product Form
The theory of free-choice Petri nets is an established field, initiated in the 1970s by Commoner and Hack at MIT. We revisit well-formed free-choice nets (those admitting markings that are both live and bounded) and provide a new…
The study of Chemical Reaction Networks (CRN's) is a very active field. Earlier well-known results \cite{Feinberg:def_01:87, Anderson:product_dist:10} identify a topological quantity called deficiency, for any CRN, which, when exactly equal…
In a previous paper we introduced immediate observation (IO) Petri nets, a class of interest in the study of population protocols and enzymatic chemical networks. In the first part of this paper we show that IO nets are globally flat, and…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
Autocatalytic chemical reaction networks can collectively replicate or maintain their constituents despite degradation reactions only above a certain threshold, which we refer to as the decay threshold. When the chemical network has a…
It is well established that resource failure, including robots and machines, in a manufacturing system can result in deadlocks. This issue not only hampers the system's performance but can also inflict significant damage on the…
A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. This paper explores the class of marked Petri nets that…
A reaction network together with a choice of rate constants uniquely gives rise to a system of differential equations, according to the law of mass-action kinetics. On the other hand, different networks can generate the same dynamical…
Product-form stationary distributions in Markov chains have been a foundational advance and driving force in our understanding of stochastic systems. In this paper, we introduce a new product-form relationship that we call "graph-based…
We consider discrete-space continuous-time Markov models of reaction networks and provide sufficient conditions for the following stability condition to hold: each state in a closed, irreducible component of the state space is positive…
In this short note, we are interested in discussing characteristics of finite generating sets for $\mathcal{F}$, the set of all semiflows with non negative coefficients of a Petri Net. By systematically positioning these results over semi…
We prove that under a multi-scale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-form limit. Each component in the product form follows an…
Place/transition Petri nets are a standard model for a class of distributed systems whose reachability spaces might be infinite. One of well-studied topics is the verification of safety and liveness properties in this model; despite the…
Synthesis for a type $\tau$ of Petri nets is the following search problem: For a transition system $A$, find a Petri net $N$ of type $\tau$ whose state graph is isomorphic to $A$, if there is one. To determine the computational complexity…
Detectability describes the property of a system whose current and the subsequent states can be uniquely determined after a finite number of observations. In this paper, we developed a novel approach to verifying strong detectability and…
A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. Characterizing the class of systems that are lucent is…
Petri networks and network models are two frameworks for the compositional design of systems of interacting entities. Here we show how to combine them using the concept of a "catalyst": an entity that is neither destroyed nor created by any…
Petri nets provide accurate analogues to chemical reaction networks, with places representing individual molecules (the resources of the system) and transitions representing chemical reactions which convert educt molecules into product…
This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions,…
We give a definition of $\mathsf{Q}$-net, a generalization of Petri nets based on a Lawvere theory $\mathsf{Q}$, for which many existing variants of Petri nets are a special case. This definition is functorial with respect to change in…