Unfolding semantics of graph transformation

Baldan, Paolo; Corradini, Andrea; Montanari, Ugo; Ribeiro, Leila

doi:10.1016/j.ic.2006.11.004

Cited by 23 publications

(45 citation statements)

References 32 publications

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“…This is in analogy to Petri nets where we regard the latter as a set of transitions with an initial marking. More precisely, as described in detail in [4], the token game of a Petri net with place set P can be modelled by spo rewriting in the slice category S↓ P , where S is the category of (finite) sets and functions: multisets are encoded as functions with co-domain P . Abstracting away from sets, we work in the slice category C↓T for a given "place" object T , also called type object.…”

Section: Grammars and Grammar Morphisms As Simulationsmentioning

confidence: 99%

“…a grammar morphism will describe how the target grammar can simulate the source grammar. Concerning the second property, the proposed notion of morphism is more concrete: for example, when C is the category of graphs, a graph grammar morphism of [4] might be induced by several different ones according to our definition. However, this greater explicitness allows to characterize the unfolding as a coreflection without restricting to the so-called semi-weighted grammars (cf.…”

Section: Definition 12 (Finite Grammarmentioning

confidence: 99%

“…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%

“…it can be expressed as a functor that is right adjoint to the embedding of the category of occurrence grammars, the category where unfoldings live, into the category of all grammars. 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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Section: Grammars and Grammar Morphisms As Simulationsmentioning

confidence: 99%

Section: Definition 12 (Finite Grammarmentioning

confidence: 99%

“…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%

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Unfolding Grammars in Adhesive Categories

Baldan

Corradini

Heindel

et al. 2009

Algebra and Coalgebra in Computer Science

Self Cite

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“…The price to pay was the introduction of more complex event structures [3,28,2,4,5]. Significantly related is also [1].…”

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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