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Contextual petri nets, asymmetric event structures and processes
 Information and Computation
, 2001
"... We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (readonly operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structure ..."
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Cited by 42 (16 self)
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We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (readonly operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskel’s seminal work on safe nets, the truly concurrent event based semantics of contextual nets is given at categorical level via a chain of coreflections
Normal Forms for Partitions and Relations
 Recent Trends in Algebraic Development Techniques, volume 1589 of Lect. Notes in Comp. Science
, 1999
"... Recently there has been a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards their application in the "distributed and concurrent systems" ..."
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Cited by 14 (11 self)
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Recently there has been a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards their application in the "distributed and concurrent systems" field, but an exhaustive comparison between them is difficult because their presentations can be quite dissimilar. This work is a first step towards a unified view, which is able to recast all those formalisms into a more general one, where they can be easily compared. We introduce a general schema for describing a characteristic normal form for many algebraic formalisms, and show that those normal forms can be thought of as arrows of suitable concrete monoidal categories.
Algebraic Models for Contextual Nets
, 2000
"... 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. ..."
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Cited by 8 (4 self)
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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.
On the Algebraic Structure of Petri Nets
 Bulletin of EATCS
, 2000
"... 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. ..."
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Cited by 7 (1 self)
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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.
Synthesising and Verifying MultiCore Parallelism in Categories of Nested Code Graphs
, 2008
"... We present the MultiCore layer of the larger Coconut project to support highperformance, highassurance scientific computation. Programs are represented by nested code graphs, using domain specific languages. At the MultiCore level, the language is very restricted, in order to restrict control fl ..."
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Cited by 2 (0 self)
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We present the MultiCore layer of the larger Coconut project to support highperformance, highassurance scientific computation. Programs are represented by nested code graphs, using domain specific languages. At the MultiCore level, the language is very restricted, in order to restrict control flow to nonbranching, synchronising control flow, which allows us to treat multicore parallelism in essentially the same way as instructionlevel parallelism for pipelined multiissue processors. The resulting schedule is then presented as a “locally sequential program”, which, like highquality conventional assembly code in the singlecore case, is arranged for hiding latencies at execution time so that peak performance can be reached, and can also be understood by programmers. We present an efficient, incremental algorithm capable of verifying the soundness of the communication aspects of such programs.
Unifying Petri nets with restricted occurrence rule using partial algebra
, 2001
"... The aim of this paper is to present a unifying concept for Petri nets with restricted occurrence rule, to obtain nonsequential semantics in a systematic way. It is shown that partial algebra is a suitable basis for process construction. Restrictions of the occurrence rule are translated into restri ..."
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The aim of this paper is to present a unifying concept for Petri nets with restricted occurrence rule, to obtain nonsequential semantics in a systematic way. It is shown that partial algebra is a suitable basis for process construction. Restrictions of the occurrence rule are translated into restrictions of concurrent composition of processes. We illustrate this claim on several wellknown examples, including context and capacity restrictions. For elementary nets with context we show the onetoone correspondence between processes constructed using partial algebra and partial order based processes.
History Preserving Bisimulation for Contextual Nets ⋆
"... Abstract. We investigate the notion of history preserving bisimulation [15,18,3] for contextual P/T nets, a generalization of ordinary P/T Petrinetswhereatransitionmaycheckforthepresenceoftokenswithout consuming them (nondestructive read operations). A first equivalence, simply called HPbisimulati ..."
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Abstract. We investigate the notion of history preserving bisimulation [15,18,3] for contextual P/T nets, a generalization of ordinary P/T Petrinetswhereatransitionmaycheckforthepresenceoftokenswithout consuming them (nondestructive read operations). A first equivalence, simply called HPbisimulation, is based on Winskel’s prime event structures. A finer equivalence, called RHPbisimulation (where “R ” stands for “read”), relies on asymmetric event structures [1], a generalization of prime event structures which gives a more faithful account of the dependencies among transition occurrences arising in contextual net computations. Extending the work in [11,19], we show that HPbisimulation is decidable for finite nsafe contextual nets. Moreover by resorting to causal automata [12] — a variation of ordinary automata introduced to deal with history dependent formalisms — we can obtain an algorithm for deciding HPbisimulation and for getting a minimal realization. Decidability of RHPbisimulation, instead, remains an open question. 1
Petri nets are dioids
, 2008
"... In a seminal paper Montanari and Meseguer showed that an algebraic interpretation of Petri nets in terms of commutative monoids can be used to provide an elegant characterisation of the deterministic computations of a net, accounting for their sequential and parallel composition. Here we show that, ..."
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In a seminal paper Montanari and Meseguer showed that an algebraic interpretation of Petri nets in terms of commutative monoids can be used to provide an elegant characterisation of the deterministic computations of a net, accounting for their sequential and parallel composition. Here we show that, along the same lines, by adding an (idempotent) operation and thus taking dioids (commutative semirings) rather than monoids, one can faithfully characterise the nondeterministic computations of a Petri net.
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"... Some algebraic laws for spans (and their connections with multirelations) 1 ..."
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Some algebraic laws for spans (and their connections with multirelations) 1