DPO Transformation with Open Maps

Heckel, Reiko

doi:10.1007/978-3-642-33654-6_14

Cited by 11 publications

(15 citation statements)

References 7 publications

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“…From the GTS side, the theory of site graph rewriting had long been thought to be a lucky anomaly until a recent series of work showed that most of its ingredients could be made sense of, and given a much larger basis of applications, through the use of algebraic graph-rewriting techniques [23,2,24]. These latter investigations motivated us to try to address these questions at a higher level of generality [9].…”

Section: Related Workmentioning

confidence: 99%

Moment Semantics for Reversible Rule-Based Systems

Danos

Heindel

Honorato-Zimmer

et al. 2015

Reversible Computation

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Abstract. We develop a notion of stochastic rewriting over marked graphs -i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the 'no-dangling-edge' condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions -or motif functions -form an algebra which is closed under the infinitesimal generator of (the Markov chain associated with) any such rewriting system. This gives a general procedure to derive the moment semantics of any such rewriting system, as a countable (and recursively enumerable) system of differential equations indexed by motif functions. The differential system describes the time evolution of moments (of any order) of these motif functions under the rewriting system. We illustrate the semantics using the example of preferential attachment networks; a well-studied complex system, which meshes well with our notion of marked graph rewriting. We show how in this case our procedure obtains a finite description of all moments of degree counts for a fixed degree.

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Section: Related Workmentioning

confidence: 99%

Moment Semantics for Reversible Rule-Based Systems

Danos

Heindel

Honorato-Zimmer

et al. 2015

Reversible Computation

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“…Absence of structure in L acts like a negative application condition. In [16], such conditions were characterised categorically as open maps (used earlier to describe functional bisimulations [17]). …”

Section: Matches As Open Mapsmentioning

confidence: 99%

“…Rather than restricting matches to ensure preservation of constraints such as rigidity, constraints were incorporated into the construction of a transformation as a pushout of partial maps. Instead, we follow [16] in using a double-pushout approach which defines constraints on matches to preserve rigidity. Solutions for (causal) trace compressions introduced in [4] have been reunderstood categorically in [3] using fibrations.…”

Section: Related Workmentioning

confidence: 99%

Transformation and Refinement of Rigid Structures

Danos

Heckel

Sobociński

2014

Graph Transformation

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Abstract. Stochastic rule-based models of networks and biological systems are hard to construct and analyse. Refinements help to produce systems at the right level of abstraction, enable analysis techniques and mappings to other formalisms. Rigidity is a property of graphs introduced in Kappa to support stochastic refinement, allowing to preserve the number of matches for rules in the refined system. In this paper: 1) we propose a notion of rigidity in an axiomatic setting based on adhesive categories; 2) we show how the rewriting of rigid structures can be defined systematically by requiring matches to be open maps reflecting structural features which ensure that rigidity is preserved; and 3) we obtain in our setting a notion of refinement which generalises that in Kappa, and allows a rule to be partitioned into a set of rules which are collectively equivalent to the original. We illustrate our approach with an example of a social network with dynamic topology.

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“…While the lifted Parallelism and Concurrency Theorems provide adequate constructions for composed rules specifying the effect of concurrent steps, a detailed analysis of possible interleavings of a transformation sequence leads to problematic effects caused by the NACs. As shown in [12], unlike the case without NACs, the notion of sequential independence among derivation steps is not stable under switching. More precisely, it is possible to find a derivation made of three direct transformations s = (s 1 ; s 2 ; s 3 ) where s 2 and s 3 are sequentially independent and to find a derivation s = (s 2 ; s 3 ; s 1 ) that is shift equivalent to s (obtained with the switchings (1 ↔ 2; 2 ↔ 3)), but where s 2 and s 3 are sequentially dependent on each other.…”

Section: Introductionmentioning

confidence: 98%

“…In order to address this problem, we introduce a restricted kind of NACs, based on incremental morphisms [12]. We first show that sequential independence is invariant under shift equivalence if all NACs are incremental.…”

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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DPO Transformation with Open Maps

Cited by 11 publications

References 7 publications

Moment Semantics for Reversible Rule-Based Systems

Moment Semantics for Reversible Rule-Based Systems

Transformation and Refinement of Rigid Structures

Transformation Systems with Incremental Negative Application Conditions

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