We prove that ω-languages of (non-deterministic) Petri nets and ω-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Turing machines which also form the class of effective...

We give a high-level overview of our recent results which extend and unify the lines of research initiated by Meseguer and Montanari under the motto “Petri nets are monoids”, and by Marti-Oliet, Meseguer and other authors in their linear logic axiomization of Petri nets. In particular, we investigate the use of rewriting logic, which was partially inspired by the two aforementioned approaches, ...

We propose a framework for the specification of infinite state systems based on Petri nets with distinguishedmayandmust-transitions (called modalities) which specify the allowed and the required behavior of refinements and hence of implementations. For any modal Petri net, we define its generated modal language specification which abstracts away silent transitions. On this basis we consider ref...

In this paper we show that it can be tested in polynomial time whether a scenario is an execution of a Petri net. This holds for a wide variety of Petri net classes, ranging from elementary nets to general inhibitor nets. Scenarios are given by causal structures expressing causal dependencies and concurrency among events. In the case of elementary nets and of place/transition nets, such causal ...

Petri Nets can be used for a retrospective analysis of a computer game story, for representing plots in serious games as well as for monitoring the course of the story, as recently demonstrated by several authors. It was not clear, however, whether Petri Nets can be used for representing plots and for their unfolding in games that feature large worlds inhabited by virtual humans. This paper dem...

We propose rewriting logic as a unifying framework for a wide range of Petri nets models. We treat in detail place/transition nets and important extensions of the basic model by individual tokens, test arcs, and time. Based on the idea that “Petri nets are monoids” suggested by Meseguer and Montanari we define a rewriting semantics that maps place/transition nets into rewriting logic specificat...

Petri Nets formalism requires standardisation to facilitate the work of researchers in this field and to enable the data exchange between different Petri Nets tools through a common format. Following this, a three-part International Standard (ISO/IEC 15909) has been developed. Part 1 is devoted to terms and definitions for Place/Transition Nets and High-Level Petri Nets. It is now completed (pu...

This paper presents three translations from Petri nets to Modeling, Simulation and Verification Language (MSVL) programs. Each translation is directed by one of the three semantics of Petri nets, namely interleaving, concurrency and max-concurrency. Further, for each translation, an equivalence relation between Petri nets and generated MSVL programs is proved. As a result, the supporting tool M...

This paper addresses the adoption of Petri Nets (PNs) in order to describe music processes. On the one hand, such formalism can be used to represent the results coming from the analysis of already existing music works. On the other hand, Petri Nets provide a formal tool to generate new music pieces. This paper is the evolution of an earlier work presented at CMMR 2005, where analytical and desc...

Petri Nets can represent static structure and dynamic change in a system, and reflect the state of a system and the development of event. It can express spread relationship of faults and identify the minimal cut sets (MCS) according to the relationship between inputs and outputs implied in the Incidence Matrix of Petri Nets. Petri Nets can also be used for qualitative analysis according to the ...