Synchronization Algebras with Mobility for Graph Transformations

2004

Recently there has been a lot of research, combining concepts of process algebra with those of the theory of graph grammars and graph transformation systems. Both can be viewed as general frameworks in which one can specify and reason about concurrent and distributed systems. There are many areas where both theories overlap and this reaches much further than just using graphs to give a graphic representation to processes.

versione 4) We introduce the Synchronised Hyperedge Environment, SHE, a tool for developing, analysing and automatically verifying distributed and concurrent systems. SHE supports a visual, declarative style of programming based on a graph rewrite system called Synchronising Graphs (SG) , a general semantical framework which has been used for interpreting various process calculi, such as Mobile Ambients, the distributed CCS and Fusion. After describing the system's architecture, we develop two applications: The first offers a simple declarative solution to the problem of syntactic unification, and shows how flexible the system is in supporting both textual and graphical representation of data. The second example is a classical problem in distributed programming: the leader election. The proposed solution is proven correct both by a mathematical proof and by automatic verification through model checking.

Electronic Notes in Theoretical Computer Science, 2006

We compare the expressive power of Hoare (i.e., CSP style) and Milner (i.e., CCS style) synchronizations for defining graph transformations in a framework where edges can perform actions on adjacent nodes to synchronize their evolutions. Furthermore, nodes can be communicated and merged. We show that the expressive powers of the two synchronization models are different, but no one is greater than the other. Finally, we show that in many interesting cases the behaviour of a synchronization model can be mimicked by the other one using suitable translations for the rewritten graphs.

Electronic Notes in Theoretical Computer Science, 2004

We analyze the relationship between Fusion Calculus and graph transformations defined in the Synchronized Hyperedge Replacement (SHR) style. In particular we show that the underlying algebraic structure is the same when the synchronization used in SHR is Milner synchronization. The main difference we see is that Fusion Calculus has an interleaving behaviour while SHR is inherently concurrent. In the paper we introduce the interleaving semantics for SHR with Milner synchronization and show that there is a complete correspondence between the operational semantics of Fusion Calculus and of SHR systems.

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 ...

2006

We present PRISMA, a parametric calculus that can be instantiated with different interaction policies, defined as synchronization algebras with mobility of names (SAMs). We define both operational semantics and observational semantics of PRISMA, showing that the second one is compositional for any SAM. We give examples based on heterogeneous SAMs, a case study on Fusion Calculus and some simple applications. Finally, we show that basic categorical tools can help to relate and to compose SAMs and PRISMA processes in an elegant way. 133 uses broadcast to send the news to subscribed recipients. We consider basic actions of the form xa y where x is the channel where the interaction is performed, a an action specifying the contribution to the interaction and y a tuple of parameters. Note the separation between the channel name and the action executed on it, which is a distinctive feature of our approach. In particular, we consider actions in and out respectively as input and output primitives for message passing, and in b and out b for broadcast. Also, we use publish and news as communication channels: the first is used for the interaction between the news provider and the server, and the latter for sending news to their recipients. Channel info is used as news value instead. Thus the server can be modeled as

Applied Mathematics and Computation, 2009

A synchronous concurrent algorithm (SCA) is a parallel deterministic algorithm based on a network of modules and channels, computing and communicating data in parallel, and synchronised by a global clock with discrete time. Many types of algorithms, computer architectures, and mathematical models of physical and biological systems are examples of SCAs. For example, conventional digital hardware is made from components that are SCAs and many computational models possess the essential features of SCAs, including systolic arrays, neural networks, cellular automata and coupled map lattices. In this paper we formalise the general concept of an SCA equipped with a global clock in order to analyse precisely (i) specifications of their spatio-temporal behaviour; and (ii) the senses in which the algorithms are correct. We start the mathematical study of SCA computation, specification and correctness using methods based on computation on manysorted topological algebras and equational logic. We show that specifications can be given equationally and, hence, that the correctness of SCAs can be reduced to the validity of equations in certain computable algebras. Since the idea of an SCA is general, our methods and results apply to each of the particular classes of algorithms and dynamical systems above.

Lecture Notes in Computer Science, 1992

jrwg@sys.uea.ac.uk

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).

2007

Many important systems like concurrent heap-manipulating programs, communication networks, or distributed algorithms are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation of states of these systems, where transitions can be conveniently described by graph transformation rules. We present a framework for the abstraction of graphs supporting abstract graph transformation. The abstraction method naturally generalises previous approaches to abstract graph transformation. The set of possible abstract graphs is finite. This has the pleasant consequence of generating a finite transition system for any start graph and any finite set of transformation rules. Moreover, abstraction preserves a simple logic for expressing properties on graph nodes. The precision of the abstraction can be adjusted according to properties expressed in this logic to be verified.