In this paper bounded model checking of asynchronous concurrent systems is introduced as a promising application area for answer set programming. As the model of asynchronous systems a generalisation of communicating automata, 1-safe Petri nets, are used. It is shown how a 1-safe Petri net and a requirement on the behaviour of the net can be translated into a logic program such that the bounded model checking problem for the net can be solved by computing stable models of the corresponding program. The use of the stable model semantics leads to compact encodings of bounded reachability and deadlock detection tasks as well as the more general problem of bounded model checking of linear temporal logic. Correctness proofs of the devised translations are given, and some experimental results using the translation and the Smodels system are presented.

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. 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.

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.

. The concatenable processes of a Petri net N can be characterized abstractly as the arrows of a symmetric monoidal category P(N ). However, this is only a partial axiomatization, since it is based on a concrete, ad hoc chosen, category of symmetries Sym N . In this paper we give a completely abstract characterization of the category of concatenable processes of N , thus yielding an axiomatic theory of the noninterleaving behaviour of Petri nets. Introduction Concatenable processes of Petri nets have been introduced in [3] to account, as their name indicates, for the issue of process concatenation. Let us briefly reconsider the ideas which led to their definition. The development of theory Petri nets, focusing on the noninterleaving aspects of concurrency, brought to the foreground various notions of process, e.g. [14, 5, 2, 12, 3]. Generally speaking, Petri net processes---whose standard version is given by the Goltz-Reisig non-sequential processes [5]---are structures needed to acc...

In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the Goltz-Reisig process semantics of Petri nets. We introduce a composition operation over open nets, characterized as a pushout in the corresponding category, suitable to model both interaction through open places and synchronization of transitions. The deterministic process semantics is shown to be compositional with respect to such composition operation. If a net Z 3 results as the composition of two nets Z 1 and Z 2 , having a common subnet Z 0 , then any two deterministic processes of Z 1 and Z 2 which "agree" on the common part, can be "amalgamated" to produce a deterministic process of Z 3 . Vice versa, any deterministic process of Z 3 can be decomposed into processes of the component nets. The amalgamation and decomposition operations are shown to be inverse to each other, leading to a bijective correspondence between the deterministic processes of Z 3 and pair of deterministic processes of Z 1 and Z 2 which agree on the common subnet Z 0 . Technically, our result is similar to the amalgamation theorem for data-types in the framework of algebraic specification. A possible application field of the proposed constructions and results is the modeling of interorganizational workflows, recently studied in the literature. This is illustrated by a running example.

Bounded model checking has been recently introduced as an efficient verification method for reactive systems. In this work we apply bounded model checking to asynchronous systems. More specifically, we translate the bounded reachability problem for 1-safe Petri nets into constrained Boolean circuit satisfiability. We consider three semantics: process, step, and interleaving semantics. We show that process semantics has often the best performance for bounded reachability checking.

When employing Petri nets to model distributed systems, one must be aware that the basic activities of each component can vary in duration and can involve smaller internal activities, i.e., that transitions are conceptually refined into transactions. We present an approach to the modeling of transactions based on zero-safe nets. They extend ordinary pt nets with a simple mechanism for transition synchronization. We show that the net theory developed under the two most diffused semantic interpretations (collective token and individual token philosophies) can be uniformly adapted to zero-safe nets. In particular, we show that each zero-safe net has associated two pt nets which represent the abstract counterparts of the modeled system according to the two philosophies. We show several applications of the framework, a distributed interpreter for zs nets based on classical net unfolding (here extended with a commit rule) and discuss some extensions to other net flavours.

. "Petri nets are monoids" is the title and the central idea of the paper [7]. It provides an algebraic approach to define both nets and their processes as terms. A crucial assumption for this concept is that arbitrary concurrent composition of processes is defined, which holds true for place/transition Petri nets where places can hold arbitrarily many tokens. This paper defines a similar concept for elementary Petri nets, which are elementary net systems with arbitrary initial marking. Since markings of elementary nets cannot be added arbitrarily, some operators are only defined partially; hence we employ concepts of partial algebra. The main result of the paper states that the semantics based on process terms agrees with the classical partial-order process semantics for elementary net systems. More precisely, we provide a syntactic equivalence notion for process terms and a bijection from according equivalence classes of process terms to isomorphism classes of partially ordered proce...