Abstract not found

Labelled transition systems are a simple yet powerful formalism for describing the operational behaviour of computing systems. They can be extended to model concurrency faithfully by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step. Petri nets (or Place/Transition nets) give rise to such step transition systems in a natural way -- the marking diagram of a Petri net is the canonical transition system associated with it. In this paper, we characterize the class of PN-transition systems, which are precisely those step transition systems generated by Petri nets. We express the correspondence between PN-transition systems and Petri nets in terms of an adjunction between a category of PN-transition systems and a category of Petri nets in which the associated morphisms are behaviour-preserving in a strong and natural sense.

The main feature of zero-safe nets is a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable places, zero-safe nets are equipped with zero places, which in an observable marking cannot contain any token. This yields the notion of transaction: a basic atomic computation, which may use zero tokens as triggers, but defines an evolution between observable markings only. The abstract counterpart of a generic zero-safe net B consists of an ordinary P/T net whose places are the stable places of B, and whose transitions represent the transactions of B. The two nets offer both the refined and the abstract model of the same system, where the former can be much smaller than the latter, because of the transition synchronization mechanism. Depending on the chosen approach -- collective vs individual token philosophy -- two notions of transaction may be defined, each leading to different operational and abstract models. Their comparison is fully dis...

We represent concurrent processes as Boolean propositions or gates, cast in the role of acceptors of concurrent behavior. This properly extends other mainstream representations of concurrent behavior such as event structures, yet is defined more simply. It admits an intrinsic notion of duality that permits processes to be viewed as either schedules or automata. Its algebraic structure is essentially that of linear logic, with its morphisms being consequence-preserving renamings of propositions, and with its operations forming the core of a natural concurrent programming language. 1

A formal approach for modeling and analyzing concurrent systems is proposed which integrates performance characteristics in the early stages of the design process. The approach relies on both stochastically timed process algebras and stochastically timed Petri nets in order to exploit their complementary advantages. The approach is instantiated to the case of EMPA (Extended Markovian Process Algebra), introduced together with the collection of its four semantics and the notion of equivalence that are required in order to implement the approach. Finally, the case study of the alternating bit protocol is presented to illustrate the adequacy of the approach. 1

. In the last few years, the semantics of Petri nets has been investigated in several di#erent ways. Apart from the classical "token game," one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. In our formal development a relevant role is played by DecOcc, a category of occurrence nets appropriately decorated to take into account the history of tokens. The structure of decorated occurrence nets at the same time provides natural unfoldings for Place/Transition (PT) nets and suggests a new notion of processes, the decorated processes, which induce on Petri nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net can be axiomatized as the arrows...

Petri Place/Transition (PT) nets are one of the most widely used models of concurrency. However, they still lack, in our view, a satisfactory semantics: on the one hand the “token game ” is too intensional, even in its more abstract interpretations in term of nonsequential processes and monoidal categories; on the other hand, Winskel’s basic unfolding construction, which provides a coreflection between nets and finitary prime algebraic domains, works only for safe nets. In this paper we extend Winskel’s result to PT nets. We start with a rather general category PTNets of PT nets, we introduce a category DecOcc of decorated (nondeterministic) occurrence nets and we define adjunctions between PTNets and DecOcc and between DecOcc and Occ, the category of occurrence nets. The role of DecOcc is to provide natural unfoldings for PT nets, i.e. acyclic safe nets where a notion of family is used for relating multiple instances of the same place. The unfolding functor from PTNets to Occ reduces to Winskel’s when restricted to safe nets, while the standard coreflection between Occ and Dom, the category of finitary prime algebraic domains, when composed with the unfolding functor above, determines a chain of adjunctions between PTNets and Dom.

In this paper we define a Stochastic Petri Net (SPN) semantics for Stochastic Process Algebras (SPAs), a recently introduced formalism that offers a novel approach for performance modeling. The proposed semantics is evaluated in terms of three criteria: Concurrency and Retrievability, as defined by Olderog for untimed net semantics, and Markov Equivalence for the stochastic aspects. 1 Introduction SPNs and SPAs have had somewhat of a common development. In both cases the original definitions (standard Petri nets and pure Process Algebra) did not include any temporal information, so that they were used only for the qualitative analysis of concurrent systems. The timing extensions of the basic formalisms also allowed one to study the quantitative properties of systems. In particular, in both SPNs and SPAs, negative exponentially distributed delays have been associated with the elementary events (transitions and actions), and it has been proved that both formalisms can be viewed as high...

Abstract. In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical “token game”, one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. More precisely, we introduce the new notion of decorated processes of Petri nets and we show that they induce on nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net N can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification.

In addition to ordinary places, called stable, zero-safe nets are equipped with zero places, which in a stable marking cannot contain any token. An evolution between two stable markings, instead, can be a complex computation called stable transaction, which may use zero places, but which is atomic when seen from stable places: no stable token generated in a transaction can be reused in the same transaction. Every zero-safe net has an ordinary Place-Transition net as its abstract counterpart, where only stable places are maintained, and where every transaction becomes a transition. The two nets allow us to look at the same system from both an abstract and a refined viewpoint. To achieve this result no new interaction mechanism is used, besides the ordinary token-pushing rules of nets. The refined zero-safe nets can be much smaller than their corresponding abstract P/T nets, since they take advantage of a transition synchronization mechanism. For instance, when transactions of unlimited l...