In the long history of Petri nets a universe of Petri nets has evolved consisting of an enormously rich theory, a wide variety of tools, and numerous successful applications and case studies in various application domains. This vast variety is not any more handable for anyone working with Petri nets, which results in the strong need of a structured access to Petri nets. This structured access h...

In this chapter we explain briefly the fundamentals of the interactive scores formalism. Then we develop a solution for implementing the ECO machine by mixing petri nets and constraints propagation. We also present another solution for implementing the ECO machine using concurrent constraint programming. Finally, we present an extension of interactive score with conditional branching.

The firing rule of Petri nets relies on a residuation operation for the commutative monoid of natural numbers. We identify a class of residuated commutative monoids, called Petri algebras, for which one can mimic the token game of Petri nets to define the behaviour of generalized Petri net whose flow relation and place contents are valued in such algebraic structures. We show that Petri algebra...

Introducing modularity in order to analyze a net means finding methods to decompose it into subnets such that properties of the net can be deduced from properties of these subnets. The aim of this paper is to develop a unified approach for deriving some of the fundamental properties of the global net from the properties of its components for certain types of Petri nets such as Place/Transition ...

In this paper we present a Petri-net-based approach to consider anticipated faults in real-time distributed systems. The proposed approach is based on Fuzzy Time G-Nets which is the integration of two Petri Nets extensions: Fuzzy Time Petri Net (timing Petri net extension) and G-Nets (Petri net extended with object oriented concepts). We also show that Fuzzy Time G-Nets can be used to represent...

Petri nets and Algebraic High-Level Nets are well-known to model parallel and concurrent systems. In this paper, we introduce the concept of Algebraic Higher-Order Nets, which allow to have dynamical tokens like graphs or (ordinary low-level) Petri nets. For this purpose, we specify graphs and Petri nets in the higher-order algebraic specification language HasCasl such that graphs and Petri net...

High availability constraints ensure a high level of operational performance that must be maintained during a contractual measurement period. Such constraints must be satisfied, particularly, for critical systems related to global security and human safety. High availability often results from material redundancies and lead to large stochastic discrete event models with numerous states. Markov ...

When a workflow contains a large number of tasks and involves complex control flow dependencies, verification can take too much time or it may even be impossible. Reduction rules can be used to abstract from certain transitions and places in a large net and thus could cut down the size of the net used for verification. Petri nets have been proposed to model and analyse workflows and Petri nets ...

The Petri Net Markup Language (PNML) is an XML-based interchange format for Petri nets. In order to support different versions of Petri nets and, in particular, future versions of Petri nets, PNML allows the definition of Petri net types. Due to this flexibility, PNML is a starting point for a standard interchange format for Petri nets. This paper discusses the design principles, the basic conc...