Finite petri nets as models for recursive causal behaviour

Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: \ud \ud B=(a.nilb.B)+c.nil. \ud \ud We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence

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

Flux Analysis in Process Models via Causality

We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly recognised model of concurrency, and state transitions of process models, seen as Petri nets. We show that we can this way extract the causal resource dependencies in simulations between individual state transitions as partial orders of events. We propose transformations on the partial orders that provide means for further analysis, and introduce a software tool, which implements these ideas. By means of an example of a published model of the Rho GTP-binding proteins, we argue that this approach can provide the substitute for flux analysis techniques on ordinary differential equation models within the stochastic setting of process algebras

A Logic for True Concurrency

We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history preserving bisimilarity, and fragments of the logic can be identified which correspond to other true concurrent behavioural equivalences in the literature: step, pomset and history preserving bisimilarity. Standard Hennessy-Milner logic, and thus (interleaving) bisimilarity, is also recovered as a fragment. We also propose an extension of the logic with fixpoint operators, thus allowing to describe causal and concurrency properties of infinite computations. We believe that this work contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences.Comment: 31 pages, a preliminary version appeared in CONCUR 201

A design model for Open Distributed Processing systems

This paper proposes design concepts that allow the conception, understanding and development of complex technical structures for open distributed systems. The proposed concepts are related to, and partially motivated by, the present work on Open Distributed Processing (ODP). As opposed to the current ODP approach, the concepts are aimed at supporting a design trajectory with several, related abstraction levels. Simple examples are used to illustrate the proposed concepts

Events in computation

SIGLEAvailable from British Library Document Supply Centre- DSC:D36018/81 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A Truly Concurrent Semantics for Reversible CCS

Reversible CCS (RCCS) is a well-established, formal model for reversible communicating systems, which has been built on top of the classical Calculus of Communicating Systems (CCS). In its original formulation, each CCS process is equipped with a memory that records its performed actions, which is then used to reverse computations. More recently, abstract models for RCCS have been proposed in the literature, basically, by directly associating RCCS processes with (reversible versions of) event structures. In this paper we propose a different abstract model: starting from one of the well-known encoding of CCS into Petri nets we apply a recently proposed approach to incorporate causally-consistent reversibility to Petri nets, obtaining as result the (reversible) net counterpart of every RCCS term