In this paper we address the following question: What type of event structures are suitable for representing the behaviour of general Petri nets? As a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called UL-event structures. We propose that UL-event structures are appropriate for capturing the behaviour of general Petri nets. Our answer is a partial one in that in the proposed event structure semantics, auto-concurrency is filtered out from the behaviour of Petri nets. It turns out that this limited event structure semantics for Petri nets is nevertheless a non-trivial and conservative extension of the (prime) event structure semantics of 1-safe Petri nets provided in [NPW]. We also show that the strong relationship between prime event structures and 1-safe Petri nets established in a categorical framework in [W3] can be extended to the present setting, provided we restrict our attention to the subclass ...

: The structure of High-level nets is studied from an algebraic and a logical point of view using Algebraic nets as an example. First the category of Algebraic nets is defined and the semantics given through an unfolding construction. Other kinds of Highlevel net formalisms are then presented. It is shown that nets given in these formalisms can be transformed into equivalent Algebraic nets. Then the semantics of nets in terms of universal constructions is discussed. A definition of Algebraic nets in terms of structured transition systems is proposed. The semantics of the Algebraic net is then given as a free completion of this structured transition system to a category. As an alternative also a sheaf semantics of nets is examined. Here the semantics of the net arises as a limit of a diagram of sheaves. Next Algebraic nets are characterized as encodings of special morphisms called foldings. Each algebraic net gives rise to a surjective morphism between Petri nets and conversely each sur...

Zero-safe nets have been introduced to extend classical Petri nets with a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable, zero-safe nets are equipped with zero places, which cannot contain any token in a stable marking . An evolution between two stable markings is called transaction and can be a complex computation that involves zero places, with the restriction that no stable token generated in a transaction can be reused in the same transaction. The abstract counterpart of a generic zerosafe net B consists of an ordinary pt net whose places are the stable places of B, and whose transitions are the transactions of B. The two nets offer 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 ...

The paper defines an algebraic tool for manipulating directed acyclic graphs (on short dags). The approach we propose combines two mathematical tools -- category theory and universal algebra -- and it allows an unitary treating of dags transformations. We show that the specification, implementation and programming of concurrent systems can be achieved by using this theory. 1 Introduction Graph transformation have been studied and applied in many fields of computer science: formal languages theory, software engineering, concurrent and distributed systems, etc. The intrinsic complexity of graphs does not allowed to find up to now an uniform formalism for studying graph transformation which to be universal accepted. In the present great efforts are doing to unify the theory of graph grammars and rewriting in order to demonstrate the potential of graph transformation to serve as a unifying paradigm for specification, implementation and programming sequential, parallel and distributed syst...