Expressive Power Of Petri Nets Research Articles

An algorithm for the minimum initial marking problem of a structurally live Petri net with inhibitor arcs

Inhibitor arcs increase the expressive power of Petri nets. However, they also make Petri net analysis more complex. Some properties of an ordinary Petri net are not always inherited in its extended version with inhibitor arcs. This paper reports a necessary and sufficient condition for deciding the structurally live property in an original Petri net and its extended one with inhibitor arcs. In addition, supposing that a net is structurally live, a natural problem is how to distribute the minimal number of tokens into the structurally live net to ensure that the marked net is live. A method is developed to find an optimal token allocation solution by putting tokens only in some key places. The algorithm can be completed within polynomial time, which overcomes the drawback of exhaustive solutions from all possible markings. Examples are given to illustrate the proposed approach. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Reduction rules for reset/inhibitor nets

Reset/inhibitor nets are Petri nets extended with reset arcs and inhibitor arcs. These extensions can be used to model cancellation and blocking. A reset arc allows a transition to remove all tokens from a certain place when the transition fires. An inhibitor arc can stop a transition from being enabled if the place contains one or more tokens. While reset/inhibitor nets increase the expressive power of Petri nets, they also result in increased complexity of analysis techniques. One way of speeding up Petri net analysis is to apply reduction rules. Unfortunately, many of the rules defined for classical Petri nets do not hold in the presence of reset and/or inhibitor arcs. Moreover, new rules can be added. This is the first paper systematically presenting a comprehensive set of reduction rules for reset/inhibitor nets. These rules are liveness and boundedness preserving and are able to dramatically reduce models and their state spaces. It can be observed that most of the modeling languages used in practice have features related to cancellation and blocking. Therefore, this work is highly relevant for all kinds of application areas where analysis is currently intractable.

Well-structured languages

This paper introduces the notion of well-structured language. A well-structured language can be defined by a labelled well-structured transition system, equipped with an upward-closed set of accepting states. That peculiar class of transition systems has been extensively studied in the field of computer-aided verification, where it has direct an important applications. Petri nets, and their monotonic extensions (like Petri nets with non-blocking arcs or Petri nets with transfer arcs), for instance, are special subclasses of well-structured transition systems. We show that the class of well-structured languages enjoy several important closure properties. We propose several pumping lemmata that are applicable respectively to the whole class of well-structured languages and to the classes of languages recognized by Petri nets or Petri nets with non-blocking arcs. These pumping lemmata allow us to characterize the limits in the expressiveness of these classes of language. Furthermore, we exploit the pumping lemmata to strictly separate the expressive power of Petri nets, Petri nets with non-blocking arcs and Petri nets with transfer arcs.

On the [formula omitted]-language expressive power of extended Petri nets

In this paper, we study the expressive power of several monotonic extensions of Petri nets. We compare the expressive power of Petri nets, Petri nets extended with non-blocking arcs and Petri nets extended with transfer arcs, in terms of ω -languages. We show that the hierarchy of expressive powers of those models is strict. To prove these results, we propose original techniques that rely on well-quasi orderings and monotonicity properties.

On the ω-language Expressive Power of Extended Petri Nets

In this paper, we study the expressive power of several monotonic extensions of Petri nets. We compare the expressive power of Petri nets, Petri nets extended with non-blocking arcs and Petri nets extended with transfer arcs, in terms of ω-languages. We show that the hierarchy of expressive powers of those models is strict. To prove these results, we propose original techniques that rely on well-quasi orderings and monotonicity properties.

Software modeling and analysis using a hierarchical object-oriented Petri net

Petri net is used widely to analyze and model various systems formally. Recently, many Petri nets mania devote their efforts to enhancing and extending the expressive power of Petri nets. One such effort is to extend Petri nets with object-oriented concepts. An object-oriented paradigm provides excellent concepts to model real-world problems. Object-oriented concepts allow us to build software systems easily, intuitively, and naturally. Although several high-level Petri nets with the concept of objects are suggested, these nets do not fully support the object-oriented concepts. In this paper, we propose a hierarchical object-oriented Petri net (HOONet). The formal syntax and semantics of HOONet are explained in detail. HOONet supports a wide range of object-oriented features including abstract, encapsulated and modularized objects, object interaction by message passing, inheritance, and ploymorphism. HOONet also supports a variety of modeling and analysis mechanisms such as incremental modeling of evolving systems, unfolding the HOONet to lower level Petri net, and incremental reachability analysis for HOONet models. We demonstrate the usefulness of HOONet by applying it to modeling and analysis with an example.

Petri nets with generalized algebra: a comparison

In the last decade we can see substantial effort to develop an abstract and uniform constructions for Petri nets. Most of such abstractions are based on algebraic characterizations of Petri nets. They work mostly over commutative monoids and their various subclasses, namely cancellative commutative monoids or cones of Abelian groups. In the paper we study relationships between Petri nets with generalized underlying algebra. More precisely, we study Petri nets over commutative monoids, cancellative commutative monoids, cones of Abelian groups, and fully ordered cones of Abelian groups. As the main result, we show that classes of reachability graphs of Petri nets over cancellative commutative monoids and cones of Abelian groups coincide (up to isomorphism). In other words, partial order on used cancellative commutative monoid plays no role in expressive power of Petri nets. However, as shows the fact that the class of reachability graphs of nets over fully ordered cones is a proper subclass of the class of reachability graphs of nets over cancellative commutative monoids, the total order on used monoids plays an important role in expressive power of Petri nets.

Specification and analysis of parallel/distributed software and systems by Petri nets with transition enabling functions

An approach for visually specifying parallel/distributed software using Petri nets (PNs) extend with transition enabling functions (TEFs) is investigated. The approach is demonstrated to be useful in the specification of decision-making activities that control distributed computing systems. PNs are employed because of their highly visual nature that can give insight into the nature of the controller of such a system and because of their analytical properties. In order to increase the expressive power of PNs, the extension of TEFs is used. The main focus is the specification and analysis of parallel/distributed software and systems. A key element of this approach is a set of rules derived to automatically transform such an extended net into a basic PN. Once the rules have been applied to transform the specification, analytical methods can be used to investigate characteristic properties of the system and validate correct operation. >