The Algebraic Structure of Petri Nets

Sassone, V.

doi:10.1142/9789812562494_0057

Cited by 4 publications

(3 citation statements)

References 52 publications

(83 reference statements)

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“…For example, in the case of concatenated and strongly concatenated processes (Sassone 1998), the conditions of processes are ordered to remove ambiguous possibilities of concatenation. In case of pre-nets (Sassone 2004), the authors use strings instead of multisets for markings. One of the main reasons why (finite) multisets of places with usual multiset addition (i.e.…”

Section: Algebraic Semantics Of Petri Nets: An Overviewmentioning

confidence: 99%

Semantics of petri nets: A comparison

Juhas¹,

Lehocki²

2007

2007 Winter Simulation Conference

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Section: Algebraic Semantics Of Petri Nets: An Overviewmentioning

confidence: 99%

Semantics of petri nets: A comparison

Juhas¹,

Lehocki²

2007

2007 Winter Simulation Conference

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“…In [2,11,17,18] Petri nets have been characterized categorically. An outcome of this line of work has been linking Petri nets to their executions in terms of functorial relationships between categories [16].…”

Section: Introductionmentioning

confidence: 99%

Executions in (Semi-)Integer Petri Nets are Compact Closed Categories

Genovese¹,

Herold²

2019

Electron. Proc. Theor. Comput. Sci.

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In this work, we analyse Petri nets where places are allowed to have a negative number of tokens. For each net we build its correspondent category of executions, which is compact closed, and prove that this procedure is functorial. We moreover exhibit a procedure to recover the original net from its category of executions, show that it is again functorial, and that this gives rise to an adjoint pair. Finally, we use compact closeness to infer that allowing negative tokens in a Petri net makes the causal relations between transition firings non-trivial, and we use this to model interesting phenomena in economics and computer science.

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“…A notion that is of special interest in this context is the notion of a process (see, for example, Goltz and Reisig (1983)) for Petri nets, in which the causality relation is explicitly represented. Processes and related notions, such as Pomsets (Pratt 1987) and Event Structures (Winskel 1980), have been studied extensively in the literature, and have turned out to be a powerful tool for the study of concurrent semantics (see, for example, Sassone (2000) and Baldan et al (1998) for a survey of some recent work on processes, and, in particular, on concatenable processes. For graph rewriting based on gluing, a process notion has been introduced in Corradini et al (1996).…”

Section: Introductionmentioning

confidence: 99%

Algebraic properties of processes for Local Action Systems

Verlinden

Janssens

2002

Math. Struct. Comp. Sci.

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Graph rewriting has been used extensively to model the behaviour of concurrent systems and to provide a formal semantics for them. In this paper, we investigate processes for Local Action Systems (LAS); LAS generalize several types of graph rewriting based on node replacement and embedding. An important difference between processes for Local Action Systems and the process notions that have been introduced for other systems, for example, Petri nets, is the presence of a component describing the embedding mechanism. The aim of the paper is to develop a methodology for dealing with this embedding mechanism: we introduce a suitable representation (a dynamic structure) for it, and then investigate the algebraic properties of this representation. This leads to a simple characterization of the configurations of a process and to a number of equational laws for dynamic structures. We illustrate the use of these laws by providing an equational proof of one of the basic results for LAS processes, namely that the construction yielding the result graph of a process behaves well with respect to the sequential composition of processes.

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The Algebraic Structure of Petri Nets

Abstract: This paper retraces, collects, and summarises the contributions of the author -both individually and in collaboration with others -on the theme of algebraic, compositional approaches to the semantics of Petri nets.

Cited by 4 publications

References 52 publications

Semantics of petri nets: A comparison

Semantics of petri nets: A comparison

Executions in (Semi-)Integer Petri Nets are Compact Closed Categories

Algebraic properties of processes for Local Action Systems

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