Decidability Issues for Petri Nets

This is a survey of some decidability results for Petri nets, covering the last three decades. The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics

Decidability of a temporal logic problem for Petri nets

AbstractThe paper solves an open problem from [4] by showing a decision algorithm for a temporal logic language L(Q′, GF). It implies the decidability of the problem of the existence of an infinite weakly fair occurence sequence for a given Petri net; thereby an open problem from [2] is solved

verifying a behavioural logic for graph transformation systems

We propose a framework for the verication of behavioural properties of systems modelled as graph transformation systems. The properties can be expressed in a temporal logic which is basically a -calculus where the state predicates are formulae of a monadic second order logic, describing graph properties. The verication technique relies on an algorithm for the construction of nite over-approximations of the unfolding of a graph transformation system

Modeling Time in Computing: A Taxonomy and a Comparative Survey

The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only in the computer science domain, but also in more traditional fields of engineering. This article surveys various approaches to the formal modeling and analysis of the temporal features of computer-based systems, with a level of detail that is suitable also for non-specialists. In doing so, it provides a unifying framework, rather than just a comprehensive list of formalisms. The paper first lays out some key dimensions along which the various formalisms can be evaluated and compared. Then, a significant sample of formalisms for time modeling in computing are presented and discussed according to these dimensions. The adopted perspective is, to some extent, historical, going from "traditional" models and formalisms to more modern ones.Comment: More typos fixe

A specification patterns system for discrete event systems analysis

As formal verification tools gain popularity, the problem arises of making them more accessible to engineers. A correct understanding of the logics used to express properties of a system's behavior is needed in order to guarantee that properties correctly encode the intent of the verification process. Writing appropriate properties, in a logic suitable for verification, is a skillful process. Errors in this step of the process can create serious problems since a false sense of safety is gained with the analysis. However, when compared to the effort put into developing and applying modeling languages, little attention has been devoted to the process of writing properties that accurately capture verification requirements. In this paper we illustrate how a collection of property patterns can help in simplifying the process of generating logical formulae from informally expressed requirements

Modelchecking counting properties of 1-safe nets with buffers in paraPSPACE

We consider concurrent systems that can be modelled as $1$-safe Petri nets communicating through a fixed set of buffers (modelled as unbounded places). We identify a parameter $ben$, which we call ``benefit depth\u27\u27, formed from the communication graph between the buffers. We show that for our system model, the coverability and boundedness problems can be solved in polynomial space assuming $ben$ to be a fixed parameter, that is, the space requirement is $f(ben)p(n)$, where $f$ is an exponential function and $p$ is a polynomial in the size of the input. We then obtain similar complexity bounds for modelchecking a logic based on such counting properties. This means that systems that have sparse communication patterns can be analyzed more efficiently than using previously known algorithms for general Petri nets

On the decidability of model checking LTL fragments in monotonic extensions of Petri nets

We study the model checking problem for monotonic extensions of Petri Nets, namely for two extensions of Petri nets: reset nets (nets in which places can be emptied by the firing of a transition with a reset arc) and ν-Petri nets (nets in which tokens are pure names that can be matched with equality and dynamically created). We consider several fragments of LTL for which the model checking problem is decidable for P/T nets. We first show that for those logics, model checking of reset nets is undecidable. We transfer those results to the case of ν-Petri nets. In order to cope with these negative results, we define a weaker fragment of LTL, in which negation is not allowed. We prove that for that fragment, the model checking of both reset nets and ν-Petri nets is decidable, though with a non primitive recursive complexity. Finally, we prove that the model checking problem for a version of that fragment with universal interpretation is undecidable even for P/T nets