Unfolding Grammars in Adhesive Categories

Baldan, Paolo; Corradini, Andrea; Heindel, Tobias; König, Barbara; Sobociński, Paweł

doi:10.1007/978-3-642-03741-2_24

Cited by 15 publications

(23 citation statements)

References 19 publications

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“…pullbacks 5 ; we shall make extensive use of it in this paper and it also essential for the good behaviour of grammar morphisms (see [1]). This lemma implies that, in categories with pullbacks, any fpbc square can be pulled back along a morphism with the "tip" of the square as codomain.…”

Section: Example 1 (Implicit Deletion As Fpbc)mentioning

confidence: 99%

Reversible Sesqui-Pushout Rewriting

Danos

Heindel

Honorato-Zimmer

et al. 2014

Lecture Notes in Computer Science

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Abstract. The paper proposes a variant of sesqui-pushout rewriting (SqPO) that allows one to develop the theory of nested application conditions (NACs) for arbitrary rule spans; this is a considerable generalisation compared with existing results for NACs, which only hold for linear rules (w.r.t. a suitable class of monos). Besides this main contribution, namely an adapted shifting construction for NACs, the paper presents a uniform commutativity result for a revised notion of independence that applies to arbitrary rules; these theorems hold in any category with (enough) stable pushouts and a class of monos rendering it weak adhesive HLR. To illustrate results and concepts, we use simple graphs, i.e. the category of binary endorelations and relation preserving functions, as it is a paradigmatic example of a category with stable pushouts; moreover, using regular monos to give semantics to NACs, we can shift NACs over arbitrary rule spans.

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Section: Example 1 (Implicit Deletion As Fpbc)mentioning

confidence: 99%

Reversible Sesqui-Pushout Rewriting

Danos

Heindel

Honorato-Zimmer

et al. 2014

Lecture Notes in Computer Science

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“…Together with e 2 being a mono (see above) we conclude that e 2 is an isomorphism, because adhesive categories are balanced [16]. This means, there exists a mediating morphismL 3 Fig. 3 we replace rule p 3 by rule p 4 of Fig.…”

Section: D1mentioning

confidence: 80%

“…Next, the unfolding of a GTS was defined as a typically infinite non-deterministic process which summarises all the possible derivations of a GTS [4]. Recently, all these concepts have been generalised to transformation systems based on (M-)adhesive categories [8,5,3].…”

Section: Introductionmentioning

confidence: 99%

Transformation Systems with Incremental Negative Application Conditions

Corradini

Heckel

Hermann

et al. 2013

Recent Trends in Algebraic Development Techniques

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Abstract. In several application areas, Graph Transformation Systems (GTSs) are equipped with Negative Application Conditions (NACs) that specify "forbidden contexts", in which the rules shall not be applied. The extension to NACs, however, introduces inhibiting effects among transformation steps that are not local in general, causing a severe problem for a concurrent semantics. In fact, the relation of sequential independence among derivation steps is not invariant under switching, as we illustrate with an example. We first show that this problem disappears if the NACs are restricted to be incremental. Next we present an algorithm that transforms a GTS with arbitrary NACs into one with incremental NACs only, able to simulate the original GTS. We also show that the two systems are actually equivalent, under certain assumptions on NACs.

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“…We also believe that this work can be generalized to rewriting in adhesive categories if we use a sesqui-pushout-like setting, as described in [6]. This would require to single out for a given rewriting system, a set of "atomic" subobjects from which any rewritten object can be built, playing the role of places.…”

Section: Finite Prefix For Graph Transformation Systemsmentioning

confidence: 99%

On the Computation of McMillan’s Prefix for Contextual Nets and Graph Grammars

Baldan

Bruni

Corradini

et al. 2010

Lecture Notes in Computer Science

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Abstract. In recent years, a research thread focused on the use of the unfolding semantics for verification purposes. This started with a paper by McMillan, which devises an algorithm for constructing a finite complete prefix of the unfolding of a safe Petri net, providing a compact representation of the reachability graph. The extension to contextual nets and graph transformation systems is far from being trivial because events can have multiple causal histories. Recently, we proposed an abstract algorithm that generalizes McMillan's construction to bounded contextual nets without resorting to an encoding into plain P/T nets. Here, we provide a more explicit construction that renders the algorithm effective. To allow for an inductive definition of concurrency, missing in the original proposal and essential for an efficient unfolding procedure, the key intuition is to associate histories not only with events, but also with places. Additionally, we outline how the proposed algorithm can be extended to graph transformation systems, for which previous algorithms based on the encoding of read arcs would not be applicable.

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Unfolding Grammars in Adhesive Categories

Cited by 15 publications

References 19 publications

Reversible Sesqui-Pushout Rewriting

Reversible Sesqui-Pushout Rewriting

Transformation Systems with Incremental Negative Application Conditions

On the Computation of McMillan’s Prefix for Contextual Nets and Graph Grammars

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