Local Confluence for Rules with Nested Application Conditions

Ehrig, Hartmut; Habel, Annegret; Lambers, Leen; Orejas, Fernando; Golas, Ulrike

doi:10.1007/978-3-642-15928-2_22

Cited by 20 publications

(44 citation statements)

References 15 publications

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“…We give a short review of nested application conditions before we demonstrate that conditions can be moved freely between left and right-hand sides of rules as in previous work on dpo rewriting with linear rules [13,10]. Before we recall the full definition of nacs, we informally describe a simple example.…”

Section: On Nested Application Conditionsmentioning

confidence: 99%

“…Kappa also supports a quantitative analysis that approximates the evolution of the expected number of occurrences of a given set of observable graphs over time using a system of differential equations [5]; if we want to formalise observables as graphs with a nac, we also need to keep track of the change in their occurrence counts for this quantitative analysis. This is the point where the shifting constructions for nacs as formulated in the literature [13,10] are the tool of choice. One might also consider extending this type of quantitative analysis to process calculi (via graphical encodings), in which case merging rules, as supported by the sqpo approach, become relevant, e.g.…”

Section: Introductionmentioning

confidence: 99%

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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: On Nested Application Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reversible Sesqui-Pushout Rewriting

Danos

Heindel

Honorato-Zimmer

et al. 2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Moreover, if p 0 is the empty rule, this is the Parallelism Theorem in [16], since the transformations are parallel independent for an empty kernel match. p0, m0 p1, m1 p2, m2 p1, m3 Fig.…”

Section: Theorem 2 (Multi-amalgamation) Consider a Bundle Of Kernel mentioning

confidence: 99%

“…We have that p 1 ∼ = p 0 * E p 1 . The analysis part of the Concurrency Theorem [16] now implies the decomposition into G = p0,m0…”

Section: Definition 2 (Complement Rule) Given Rulesmentioning

confidence: 99%

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Multi-Amalgamation in Adhesive Categories

Golas

Ehrig

Habel

2010

Lecture Notes in Computer Science

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Abstract. Amalgamation is a well-known concept for graph transformations in order to model synchronized parallelism of rules with shared subrules and corresponding transformations. This concept is especially important for an adequate formalization of the operational semantics of statecharts and other visual modeling languages, where typed attributed graphs are used for multiple rules with general application conditions. However, the theory of amalgamation for the double pushout approach has been developed up to now only on a set-theoretical basis for pairs of standard graph rules without any application conditions. For this reason, we present the theory of amalgamation in this paper in the framework of adhesive categories for a bundle of rules with (nested) application conditions. In fact, it is also valid for weak adhesive HLR categories. The main result is the Multi-Amalgamation Theorem, which generalizes the well-known Parallelism and Amalgamation Theorems to the case of multiple synchronized parallelism. The constructions are illustrated by a small running example. A more complex case study for the operational semantics of statecharts based on multi-amalgamation is presented in a separate paper.

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Initial Conflicts for Transformation Rules with Nested Application Conditions

Lambers

Orejas

2020

Graph Transformation

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We extend the theory of initial conflicts in the framework of M-adhesive categories to transformation rules with ACs. We first show that for rules with ACs, conflicts are in general neither inherited from a bigger context any more, nor is it possible to find a finite and complete subset of finite conflicts as illustrated for the category of graphs. We define initial conflicts to be special so-called symbolic transformation pairs, and show that they are minimally complete (and in the case of graphs also finite) in this symbolic way. We show that initial conflicts represent a proper subset of critical pairs again. We moreover demonstrate that (analogous to the case of rules without ACs) for each conflict a unique initial conflict exists representing it. We conclude with presenting a sufficient condition illustrating important special cases for rules with ACs, where we do not only have initial conflicts being complete in a symbolic way, but also find complete (and in the case of graphs also finite) subsets of conflicts in the classical sense.

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Local Confluence for Rules with Nested Application Conditions

Cited by 20 publications

References 15 publications

Reversible Sesqui-Pushout Rewriting

Reversible Sesqui-Pushout Rewriting

Multi-Amalgamation in Adhesive Categories

Initial Conflicts for Transformation Rules with Nested Application Conditions

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