On the semantics of place/transition Petri nets

Meseguer, José; Montanari, Ugo; Sassone, Vladimiro

doi:10.1017/s0960129597002314

Cited by 42 publications

(39 citation statements)

References 39 publications

(74 reference statements)

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“…However, this greater explicitness allows to characterize the unfolding as a coreflection without restricting to the so-called semi-weighted grammars (cf. [18,4,1]). …”

Section: Definition 12 (Finite Grammarmentioning

confidence: 99%

“…In order to define the category of grammars we introduce an original notion of grammar morphism which is similar to the graph grammar morphisms proposed in [4] but more concrete; as a consequence, we can treat uniformly the whole class of grammars, without the need to restrict to so-called semi-weighted grammars as it was done in several approaches for Peri nets (see, e.g. [18]) and for graph grammars [4].…”

Section: Introductionmentioning

confidence: 99%

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Unfolding Grammars in Adhesive Categories

Baldan

Corradini

Heindel

et al. 2009

Algebra and Coalgebra in Computer Science

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Abstract. We generalize the unfolding semantics, previously developed for concrete formalisms such as Petri nets and graph grammars, to the abstract setting of (single pushout) rewriting over adhesive categories. The unfolding construction is characterized as a coreflection, i.e. the unfolding functor arises as the right adjoint to the embedding of the category of occurrence grammars into the category of grammars. As the unfolding represents potentially infinite computations, we need to work in adhesive categories with "well-behaved" colimits of ω-chains of monomorphisms. Compared to previous work on the unfolding of Petri nets and graph grammars, our results apply to a wider class of systems, which is due to the use of a refined notion of grammar morphism.

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“…However, this greater explicitness allows to characterize the unfolding as a coreflection without restricting to the so-called semi-weighted grammars (cf. [18,4,1]). …”

Section: Definition 12 (Finite Grammarmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unfolding Grammars in Adhesive Categories

Baldan

Corradini

Heindel

et al. 2009

Algebra and Coalgebra in Computer Science

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“…Indeed alternative categories of net systems have been studied -see, e.g., [93,45,12,48,97]. Here we just remark that Proposition 1.5 proves that these morphisms preserve behaviour (and concurrency), a fact that has been explored by, e.g.…”

Section: Definitionmentioning

confidence: 93%

“…In our presentation we have chosen to treat (only) three different classes of net systems: the elementary net systems of Thiagarajan [87], the semiweighted net systems [48], and place/transition systems [72], but the approaches presented here are, we claim, applicable to any class of net systems.…”

Section: Introductionmentioning

confidence: 99%

Petri nets and other models of concurrency

Nielsen

Sassone

1998

Lectures on Petri Nets I: Basic Models

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“…The title itself is revealing: Petri nets are monoids. Besides doing what it says on the tin, this paper opened a long-lasting and fruitful collaboration with José Meseguer, and a research line on the initial semantics of computational models in which, after [33], we got deeply involved ourselves [55,56,17,24,18]. The key insight is that by lifting the algebraic structure of (machine) states to the level of computations via a so-called free construction, one can gain a deeper understanding of the axioms which regulate equivalent computations (or processes), an idea that is also the basis of Meseguer's Rewriting Logic [51].…”

Section: Ugo Montanari's Models Of Computationmentioning

confidence: 99%

Models of Computation: A Tribute to Ugo Montanari’s Vision

Bruni

Sassone

2008

Concurrency, Graphs and Models

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Ugo's research activity in the area of Models of Computation (MoC, for short) has been prominent, influential and broadly scoped. Ugo's trademark is that undefinable ability to understand and distill computational aspects into new models as if you were reading them out of some evident connection between well-know models: only, most often, that connection is really visible only after Ugo shows the way. Like experienced sailors have trusted compasses and sextants to help them find the best routes to harbour, Ugo relies on a bag of favourite tools which he has used along the years to deliver a variety of contributions to the MoC area. To mention just three (in alphabetic order): algebraic techniques, concurrency theory, and unification mechanisms.In this introductory contribution we would like to recall some of the influential MoC models put forward by Ugo which cut across the three approaches. Before doing that, it is worth devoting some space to discuss the three aspects separately. Notably, the use of category theory is a pervasive common trait.Algebraic techniques. By algebraic techniques we refer broadly to the use of universal algebras and initial model semantics; of universal coalgebras and final semantics; and of bialgebras. Many interesting papers witness Ugo's leading role in exploiting algebraic techniques during his entire scientific career. Indeed, his contributions are too many to mention all in the space allocated to this overview; we shall therefore attempt to convey the sense of Ugo's broad-spectrum contribution by recapping only a few key results.Reference [43] is the first paper on final, observational semantics in abstract data types, and the main reference for one of the MoC contributed papers in this volume. It presented several key insights in software specification and development for the first time, like the separation between given sorts and newly specified ones, whereby the given sorts lay the ground to define the observable behaviour for the new sorts. Another key suggestion is that the specification of new data types is often partial -in the sense that it may include "don't care" cases-and that many realisations can exist that exhibit equivalent observable behaviour but are not isomorphic. In fact, [43] shows that the isomorphism classes of observably equivalent algebras conforming to the partial specification form a complete lattice, yielding a so-called loose semantics.Possibly the best known of Ugo's papers, [52] exposes the underlying monoidal structure of the category of Petri net computations. The title itself is revealing: Petri nets are monoids. Besides doing what it says on the tin, this paper opened a long-lasting and fruitful collaboration with José Meseguer, and a research line on the initial semantics of P. Degano et al. (Eds.): Montanari

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On the semantics of place/transition Petri nets

Cited by 42 publications

References 39 publications

Unfolding Grammars in Adhesive Categories

Unfolding Grammars in Adhesive Categories

Petri nets and other models of concurrency

Models of Computation: A Tribute to Ugo Montanari’s Vision

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