The Possibilities of Modeling Petri Nets and Their Extensions

2019

Information and Control, 1977

Theoretical Computer Science, 2011

We introduce the notion of T -path within Petri nets, and propose a simple approach, based on previous work developed for directed hypergraphs, in order to determine structural properties of nets; in particular, we study the relationships between T -paths in a Petri net and firable sequences of transitions.

In this paper, we propose an extension of Petri nets suitable for control systems design and discuss its methods of evaluation. In order to study the behavior of a system mod elled with this net, we provide a means for searching the reachability tree of markings. The logical colored Petri net (LCPN) is an extended Petri net which solves the problem of system description in place/transition nets and colored P etri nets proposed before.

IEEE Transactions on Computers, 2001

AbstractÐThis work presents a symbolic approach for the analysis of bounded Petri nets. The structure and behavior of the Petri net is symbolically modeled by using Boolean functions, thus reducing reasoning about Petri nets to Boolean calculation. The set of reachable markings is calculated by symbolically firing the transitions in the Petri net. Highly concurrent systems suffer from the state explosion problem produced by an exponential increase of the number of reachable states. This state explosion is handled by using Binary Decision Diagrams (BDDs) which are capable of representing large sets of markings with small data structures. Petri nets have the ability to model a large variety of systems and the flexibility to describe causality, concurrency, and conditional relations. The manipulation of vast state spaces generated by Petri nets enables the efficient analysis of a wide range of problems, e.g., deadlock freeness, liveness, and concurrency. A number of examples are presented in order to show how large reachability sets can be generated, represented, and analyzed with moderate BDD sizes. By using this symbolic framework, properties requiring an exhaustive analysis of the reachability graph can be efficiently verified.

Lecture Notes in Computer Science, 1980

A relational model for non-deterministic programs is presented. Several predicate transformers are introduced and it is shown that one of them satisfies all the healthiness criteria indicated by Dijkstra for a useful total correctness predicate transformer.

Symbolic techniques based on Binary Decision Diagrams have emerged as one of the possible strategies to overcome the state exposition problem in the analysis of systems modeled as Petri nets. The results on structural theory of Petri nets obtained in the last few decades can be used to improve the symbolic analysis and to alleviate the state exposition problem.

A Jumping Petri Net ([18], [12]), JPTN for short, is defined as a classical net which can spontaneously jump from a marking to another one. In [18] it has been shown that the reachability problem for JPTN's is undecidable, but it is decidable for finite JPTN's (FJPTN). In this paper we establish some specific properties and investigate the computational power of such nets, via the interleaving semantics. Thus, we show that the non-labelled JPTN's have the same computational power as the labelled or #-labelled JPTN's. When final markings are considered, the power of JPTN's equals the power of Turing machines. The family of regular languages and the family of languages generated by JPTN's with finite state space are shown to be equal. Languages generated by FJPTN's can be represented in terms of regular languages and substitutions with classical Petri net languages. This characterization result leads to many important consequences, e.g. the recursiveness (c...

Cornell University - arXiv, 2022

Barwise and Seligman stated the first principle of information flow: "Information flow results from regularities in the distributed system." They represent a distributed system in terms of a classification consisting of a set of objects or tokens to be classified, a set of types used to classify tokens, and a binary relation between tokens and types that tells one which tokens are classified as being of which types. We aim to further this investigation and proceed with a dynamic or evolving system instead of a static system. We claim that a classification is a snapshot of a distributed system at a given moment or context. We then aim to answer the question posed by an evolving context. As the context or configuration changes, how do regularities evolve. This paper is a continuation of an investigation we started in [2], where we initiated how to capture a dynamism of information flow with a Kripke structure. Here we develop the same procedure with colored Petri net(CPN). We first extend the classification concept to multiclassification by replacing its binary relation between tokens and types with a multi relation: a function from tok(A) × typ(A) to N, the set of natural numbers. The multiclassification will unfold into binary classification in order to compute its theory. It turns out that markings of a CPN are multiclassification; Amalgamating the theories of those classifications obtained as markings of CPN results in a CPN's knowledge base.

Lecture Notes in Computer Science, 2010

We show that the downward-closure of a Petri net language is effectively computable. This is mainly done by using the notions defined for showing decidability of the reachability problem of Petri nets. In particular, we rely on Lambert's construction of marked graph transition sequences-special instances of coverability graphs that allow us to extract constructively the simple regular expression corresponding to the downward-closure. We also consider the remaining language types for Petri nets common in the literature. For all of them, we provide algorithms that compute the simple regular expressions of their downwardclosure. As application, we outline an algorithm to automatically analyse the stability of a system against attacks from a malicious environment.