Characterizing behavioural congruences for Petri nets

Nielsen, Mogens; Priese, Lutz; Sassone, Vladimiro

doi:10.1007/3-540-60218-6_13

Cited by 29 publications

(32 citation statements)

References 21 publications

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“…Nielsen, Priese and Sassone [40] characterise some behavioural congruences on nets. Given a semantic function B that assigns an abstract behaviour to each net, they consider the congruence ≈ it induces upon nets; this is defined by…”

Section: Condition-event Nets As Link Graphsmentioning

confidence: 99%

Transition systems, link graphs and Petri nets

Leifer

Milner

2006

Math. Struct. in Comp. Science

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A framework is defined within which reactive systems can be studied formally. The framework is based upon s-categories, a new variety of categories, within which reactive systems can be set up in such a way that labelled transition systems can be uniformly extracted. These lead in turn to behavioural preorders and equivalences, such as the failures preorder (treated elsewhere) and bisimilarity, which are guaranteed to be congruential. The theory rests upon the notion of relative pushout previously introduced by the authors.The framework is applied to a particular graphical model known as link graphs, which encompasses a variety of calculi for mobile distributed processes. The specific theory of link graphs is developed. It is then applied to an established calculus, namely condition-event Petri nets.In particular, a labelled transition system is derived for condition-event nets, corresponding to a natural notion of observable actions in Petri net theory. The transition system yields a congruential bisimilarity coinciding with one derived directly from the observable actions. This yields a calibration of the general theory of reactive systems and link graphs against known specific theories.

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Section: Condition-event Nets As Link Graphsmentioning

confidence: 99%

Transition systems, link graphs and Petri nets

Leifer

Milner

2006

Math. Struct. in Comp. Science

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“…Also coloured and reconfigurable nets are, of course, special kinds of dynamic nets. The characteristic feature of dynamic nets, that to our best knowledge distinguishes them by other approaches in the literature and draws a connection to [13], is that, as for reconfigurable nets, input arcs are never modified. While it is possible to modify dynamically the post-set of a transition, and also to spawn new subnets, it is not possible to add places to the presets of transitions.…”

Section: Dynamic Netsmentioning

confidence: 99%

“…But they cannot change the input arcs of any transitions. As in [13], where an algebra with such properties has been considered, we believe that this is the key to a tractable compositional semantic framework, the key to control generality. Most noticeably, it corresponds to unique receptiveness in the join calculus.…”

Section: Introductionmentioning

confidence: 99%

High-Level Petri Nets as Type Theories in the Join Calculus

Buscemi

Sassone

2001

Lecture Notes in Computer Science

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Abstract. We study the expressiveness of the join calculus by comparison with (generalised, coloured) Petri nets and using tools from type theory. More precisely, we consider four classes of nets of increasing expressiveness, Π i, introduce a hierarchy of type systems of decreasing strictness, ∆i, i = 0, . . . , 3, and we prove that a join process is typeable according to ∆i if and only if it is (strictly equivalent to) a net of class Πi. In the details, Π0 and Π1 contain, resp., usual place/transition and coloured Petri nets, while Π2 and Π3 propose two natural notions of high-level net accounting for dynamic reconfiguration and process creation and called reconfigurable and dynamic Petri nets, respectively.

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“…And in fact, the literature is rich of examples of process algebras over nets, as, e.g., [54,27,8,51,58] (see also the early [19, 13, 99, 38, 70] on compositionality issues). Observe that category theory can clearly play an interesting role in this, as we are called to consider the totality of nets, as in Part 1, focusing this time -as in Part 2 -on algebraic and compositional aspects.…”

Section: Conclusion and Related Workmentioning

confidence: 99%