Synchronized Hyperedge Replacement for Heterogeneous Systems

Synchronising Graphs is a system of parallel graph trans- formation designed for modeling process interaction in a network envi- ronment. Although notions of observational equivalence are abundant in the literature for process calculi, not so for graph rewriting, where system behaviour is typically context dependent. We propose a theory of context-free synchronising graphs and a novel notion of bisimulation equivalence which is shown to be a congruence with respect to graph composition and node restriction. This notion is used to provide a proof technique for the hyperequivalence of the Fusion calculus, through an en- coding which is shown to be sound and complete. This builds a bridge between graph rewriting and process algebra. As a further application, we prove the correctness of a system component, called non-deterministic commuter, with respect to its specification. The result shows that our notion of equivalence is fine enough to discriminate between dierent degrees of paralle...

Lecture Notes in Computer Science, 1993

In this paper, we introduce and study a rendezvous mechanism for parallel replacements of hyperedges by (hyperedge-decorated) graphs that allows some merging of the replacing graphs if the attachment of the replaced hyperedges shares some nodes. The main result shows that the rendezvous mechanism can increase the generative power of table-controlled parallel hyperedge replacement graph grammars (which themselves are more powerful than ordinary hyperedge replacement graph grammars). 1.2 Definition (decorated graph) Let N be a set of nonterminal labels each element A of which is associated with a natural nmnber, its type, denoted by type(A).

2014

The goal of the present document is to support the taxonomy for bidirectional model synchronization developed in [1] with a formal semantics. The taxonomy is 3D so that each synchronization type is characterized by a triple of coordinates (x, y, z), in which x classifies the organizational symmetry of the case, y is for the informational symmetry, and z is for incrementality of the update propagation operations. Different types of delta lenses (algebraic structures modeling bx) can be classified by points on the YZ-plane. As for the x-coordinate, it says, roughly, whether update propagation is unior bi-directional, but as it was shown in [1], there are several important refinements of the twovalued uni, bi-classification so that actually axis X has four rather than two points. A formal semantics for the enriched X-classification seems to be an entirely novel aspect for the (delta) lens literature. There are also several contributions for the very delta lens framework within the plan...

2004

In graph-based systems there are many methods to compose (possibly different) graphs. However, none of these usual compositions are adequate to naturally express semantics of systems with dynamic topology, i.e., systems whose topology admits successive transformations through its computation. We constructed a categorical semantic domain for graph based systems with dynamic topology using a new way to compose edges of (possible different) graphs. In this context, sequences of different graphs represent successive transformations of system topology during its computation and the edges composition between those graphs, the semantics of the corresponding dynamic system. Then we show how the proposed approach can be used to give semantics to concurrent anticipatory systems.

In graph-based systems there are many methods to compose (possibly different) graphs. However, none of these usual compositions are adequate to naturally express semantics of systems with dynamic topology, i.e., systems whose topology admits successive transformations through its computation. We constructed a categorical semantic domain for graph based systems with dynamic topology using a new way to compose edges of (possible different) graphs. In this context, sequences of different graphs represent successive transformations of system topology during its computation and the edges composition between those graphs, the semantics of the corresponding dynamic system. Then we show how the proposed approach can be used to give semantics to concurrent anticipatory systems.

2011

Triple graph grammars (TGGs) have been used successfully to analyze correctness and completeness of bidirectional model transformations, but a corresponding formal approach to model synchronization has been missing. This paper closes this gap by providing a formal synchronization framework with bidirectional update propagation operations. They are generated from a TGG, which specifies the language of all consistently integrated source and target models. As a main result, we show that the generated synchronization framework is correct and complete, provided that forward and backward propagation operations are deterministic. Correctness essentially means that the propagation operations preserve consistency. Moreover, we analyze the conditions under which the operations are inverse to each other. All constructions and results are motivated and explained by a small running example using concrete visual syntax and abstract syntax notation based on typed attributed graphs.

2008

The paper presents several algebraic models for semantics of bidirectional model synchronization and transformation. Different types of model synchronization are analyzed (view updates, selective and incremental synchronization), and this analysis motivates the formal definitions. Particularly, a new formal model of updates is proposed. Relationships between the formal models are precisely specified and discussed.

We present PRISMA, a parametric framework for modeling distributed and mobile systems with different communication policies, defined as synchronization algebras with mobility (SAMs). This allows to choose each time the SAM that corresponds to the real synchronization used, and also to prove properties for different synchronization models at once. The paradigm we propose is based on process calculi to facilitate the reuse of techniques and results from the vast literature. We define both the operational semantics and a compositional observational semantics for PRISMA. We present a detailed case study on Fusion Calculus and many different SAMs as examples. Finally, we exploit basic categorical constructions to relate and compose SAMs.

Applied Categorical Structures, 2001

The classical algebraic approach to graph transformation is a mathematical theory based on categorical techniques with several interesting applications in computer science. In this paper, a new semantics of graph transformation systems (in the algebraic, double-pushout (DPO) approach) is proposed in order to make them suitable for the specification of concurrent and reactive systems. Classically, a graph transformation system comes with a fixed behavioral interpretation. Firstly, all transformation steps are intended to be ...

Electronic Proceedings in Theoretical Computer Science, 2011

Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics (LTS). While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in general. Hence, the goal of this article is to obtain a compositional semantics for graph transformation system in analogy to the structural operational semantics (SOS) for Milner's Calculus of Communicating Systems (CCS).