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1

Mutex Causality in Processes and Traces of General Elementary Nets

Kleijn J., Koutny M.

Fundamenta Informaticae

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2013

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Vol. 122, nr 1-2

119--146

EN

A concurrent history represented by a causality structure that captures the intrinsic, invariant dependencies between its actions, can be interpreted as defining a set of closely related observations (e.g., step sequences). Depending on the relationships observed in the histories of a system, the concurrency paradigm to which it adheres may be identified, with different concurrency paradigms underpinned by different kinds of causality structures. Elementary net systems with inhibitor arcs and mutex arcs (ENIM-systems) are a system model that through its process semantics and associated causality structures fits the least restrictive concurrency paradigm. One can also investigate the abstract behaviour of an ENIM-system by grouping together step sequences in equivalence classes (generalised comtraces) using the structural relations between its transitions. The resulting concurrent histories of the ENIM-system are consistent with the generalised stratified order structures underlying its processes. The paper establishes a link between ENIM-systems and trace theory allowing one to discuss different observations of concurrent behaviour in a way that is consistent with the causality semantics defined by the operationally defined processes.

2

Complete Process Semantics of Petri Nets

Juhás G., Lorenz R., Mauser S.

Fundamenta Informaticae

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2008

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Vol. 87, nr 3-4

331-365

EN

In the first part of this paper we extend the semantical framework proposed in [22] for process and causality semantics of Petri nets by an additional aim, firstly mentioned in the habilitation thesis [15]. The aim states that causality semantics deduced from process nets should be complete w.r.t. step semantics of a Petri net in the sense that each causality structure which is enabled w.r.t. step semantics corresponds to some process net. In the second part of this paper we examine several process semantics of different Petri net classes w.r.t. this aim. While it is well known that it is satisfied by the process semantics of place/transition Petri nets (p/t-nets), we show in particular that the process semantics of p/t-nets with weighted inhibitor arcs (PTI-nets) proposed in [22] does not satisfy the aim. We develop a modified process semantics of PTI-nets fulfilling the aim of completeness and also all remaining axioms of the semantical framework. Finally, we sketch results in literature concerning the aim of completeness for process definitions of various further Petri net classes. The paper is a revised and extended version of the conference paper [18].

3

Comparing truly concurrent semantics for contextual Place/Transition nets with inhibitor and read arcs

Busi N., Pinna G.M.

Fundamenta Informaticae

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2000

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Vol. 44, Nr 3

209-244

EN

The paper is centered around the study and comparison of truly concurrent semantics for P/T nets with inhibitor and read arcs (called henceforth contextual P/T nets). We start proposing a causal semantics for P/T nets, that we prove to be equivalent to history preserving bisimulation defined on nonsequential processes. Then we develop a conservative extension of the causal semantics to contextual P/T nets and we prove this one to be finer than step semantics. Finally, a comparison of causal semantics with the process based semantics for contextual P/T systems proposed in [7] is carried out.

4

Process semantics for Place/Transition nets with inhibitor and read arcs

Busi N., Pinna G.M.

Fundamenta Informaticae

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1999

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Vol. 40, Nr 2,3

165-197

EN

In this paper we introduce a truly concurrent semantics for P/T nets with inhibitor and read arcs, called henceforth Contextual P/T nets. The semantics is based on a proper extension of the notion of process to cope with read and inhibitor arcs: we show that most of the properties enjoined by the classical process semantics for P/T nets continue to hold and we substantiate the adequateness of our notion by comparing it with the step semantics.