79 research outputs found
Algebraic Models for Contextual Nets
We extend the algebraic approach of Meseguer and Montanari from ordinary place/transition Petri nets to contextual nets, covering both the collective and the individual token philosophy uniformly along the two interpretations of net behaviors
Two Algebraic Process Semantics for Contextual Nets
We show that the so-called 'Petri nets are monoids' approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs
Event structures for Petri nets with persistence
Event structures are a well-accepted model of concurrency. In a seminal paper by Nielsen, Plotkin and Winskel, they are used to establish a bridge between the theory of domains and the approach to concurrency proposed by Petri. A basic role is played by an unfolding construction that maps (safe) Petri nets into a subclass of event structures, called prime event structures, where each event has a uniquely determined set of causes. Prime event structures, in turn, can be identified with their domain of configurations. At a categorical level, this is nicely formalised by Winskel as a chain of coreflections. Contrary to prime event structures, general event structures allow for the presence of disjunctive causes, i.e., events can be enabled by distinct minimal sets of events. In this paper, we extend the connection between Petri nets and event structures in order to include disjunctive causes. In particular, we show that, at the level of nets, disjunctive causes are well accounted for by persistent places. These are places where tokens, once generated, can be used several times without being consumed and where multiple tokens are interpreted collectively, i.e., their histories are inessential. Generalising the work on ordinary nets, Petri nets with persistence are related to a new subclass of general event structures, called locally connected, by means of a chain of coreflections relying on an unfolding construction
Catalytic and communicating Petri nets are Turing complete
In most studies about the expressiveness of Petri nets, the focus has been put either on adding suitable arcs or on assuring that a complete snapshot of the system can be obtained. While the former still complies with the intuition on Petri nets, the second is somehow an orthogonal approach, as Petri nets are distributed in nature. Here, inspired by membrane computing, we study some classes of Petri nets where the distribution is partially kept and which are still Turing complete
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An algebra of high level petri nets
PhD ThesisPetri nets were introduced by C.A. Petri as a theoretical model of concurrency in which the causal
relationship between actions, rather than just their temporal ordering, can be represented. As
a theoretical model of concurrency, Petri nets have been widely successful. Moreover, Petri nets
are popular with practitioners, providing practical tools for the designer and developer of real
concurrent and distributed systems.
However, it is from this second context that perhaps the most widely voiced criticism of Petri
nets comes. It is that Petri nets lack any algebraic structure or modularity, and this results in
large, unstructured models of real systems, which are consequently often intractable. Although
this is not a criticism of Petri nets per se, but rather of the uses to which Petri nets are put, the
criticism is well taken.
We attempt to answer this criticism in this work. To do this we return to the view of Petri nets
as a model of concurrency and consider how other models of concurrency counter this objection.
The foremost examples are then the synchronisation trees of Milner, and the traces of Hoare,
(against which such criticism is rarely, if ever, levelled). The difference between the models is
clear, and is to be found in the richness of the algebraic characterisations which have been made
for synchronisation trees in Milner's Calculus of Communicating Systems (CCS), and for traces
in Hoare's Communicating Sequential Processes (CSP).
With this in mind we define, in this thesis, a class of high level Petri nets, High Level Petri Boxes,
and provide for them a very general algebraic description language, the High Level Petri Box
Algebra, with novel ideas for synchronisation, and including both refinement and recursion among
its operators. We also begin on the (probably open-ended task of the) algebraic characterisation
of High Level Petri Boxes.
The major contribution of this thesis is a full behavioural characterisation of the High Level Petri
Boxes which form the semantic domain of the algebra. Other contributions are: a very general
method of describing communication protocols which extend the synchronisation algebras of
Winskel; a recursive operator that preserves finiteness of state (the best possible, given the
generality of the algebra); a refinement operator that is syntactic in nature, and for which the
recursive construct is a behavioural fix-point; and a notion of behavioural equivalence which is
a congruence with respect to a major part of the High Level Petri Box Algebra
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