Mapping Fusion and Synchronized Hyperedge Replacement into Logic Programming

In this paper we compare three different formalisms that can be used in the area of models for distributed, concurrent and mobile systems. In particular we analyze the relationships between a process calculus, the Fusion Calculus, graph transformations in the Synchronized Hyperedge Replacement with Hoare synchronization (HSHR) approach and logic programming. We present a translation from Fusion Calculus into HSHR (whereas Fusion Calculus uses Milner synchronization) and prove a correspondence between the reduction semantics of Fusion Calculus and HSHR transitions. We also present a mapping from HSHR into a transactional version of logic programming and prove that there is a full correspondence between the two formalisms. The resulting mapping from Fusion Calculus to logic programming is interesting since it shows the tight analogies between the two formalisms, in particular for handling name generation and mobility. The intermediate step in terms of HSHR is convenient since graph transformations allow for multiple, remote synchronizations, as required by Fusion Calculus semantics.Comment: 44 pages, 8 figures, to appear in a special issue of Theory and Practice of Logic Programming, minor revisio

Architectural design rewriting as an architecture description language

Architectural Design Rewriting (ADR) is a declarative rule-based approach for the design of dynamic software architectures. The key features that make ADR a suitable and expressive framework are the algebraic presentation of graph-based structures and the use of conditional rewrite rules. These features enable the modelling of, e.g. hierarchical design, inductively defined reconfigurations and ordinary computation. Here, we promote ADR as an Architectural Description Language

Style-Based architectural reconfigurations

We introduce Architectural Design Rewriting (ADR), an approach to the design of reconfigurable software architectures whose key features are: (i) rule-based approach (over graphs); (ii) hierarchical design; (iii) algebraic presentation; and (iv) inductively-defined reconfigurations. Architectures are modelled by graphs whose edges and nodes represent components and connection ports. Architectures are designed hierarchically by a set of edge replacement rules that fix the architectural style. Depending on their reading, productions allow: (i) top-down design by refinement, (ii) bottom-up typing of actual architectures, and (iii) well-formed composition of architectures. The key idea is to encode style proofs as terms and to exploit such information at run-time for guiding reconfigurations. The main advantages of ADR are that: (i) instead of reasoning on flat architectures, ADR specifications provide a convenient hierarchical structure, by exploiting the architectural classes introduced by the style, (ii) complex reconfiguration schemes can be defined inductively, and (iii) style-preservation is guaranteed

Ten virtues of structured graphs

This paper extends the invited talk by the first author about the virtues of structured graphs. The motivation behind the talk and this paper relies on our experience on the development of ADR, a formal approach for the design of styleconformant, reconfigurable software systems. ADR is based on hierarchical graphs with interfaces and it has been conceived in the attempt of reconciling software architectures and process calculi by means of graphical methods. We have tried to write an ADR agnostic paper where we raise some drawbacks of flat, unstructured graphs for the design and analysis of software systems and we argue that hierarchical, structured graphs can alleviate such drawbacks

Constraint Design Rewriting

We propose an algebraic approach to the design and transformation of constraint networks, inspired by Architectural Design Rewriting. The approach can be understood as (i) an extension of ADR with constraints, and (ii) an application of ADR to the design of reconfigurable constraint networks. The main idea is to consider classes of constraint networks as algebras whose operators are used to denote constraint networks with terms. Constraint network transformations such as constraint propagations are specified with rewrite rules exploiting the network’s structure provided by terms

A graph semantics for a variant of the ambient calculus more adequate for modeling SOC

In this paper we present a graph semantics of a variant of the well known ambient calculus. The main change of our variant is to extract the mobility commands of the original calculus from the ambient topology. Similar to a previous work of ours, we prove that our encoding have good properties. We strongly believe that this variant would allow us to integrate our graph semantics of our mobile calculus with previous work of us in service oriented computing (SOC). Basically, our work on SOC develops a new graph transformation system which we call temporal symbolic graphs. This new graph formalism is used to give semantics to a design language for SOC developed in an european project, but it could also be used in connection with other approaches for modeling or specifying service systems.Postprint (published version

A formal support to business and architectural design for service-oriented systems

Architectural Design Rewriting (ADR) is an approach for the design of software architectures developed within Sensoria by reconciling graph transformation and process calculi techniques. The key feature that makes ADR a suitable and expressive framework is the algebraic handling of structured graphs, which improves the support for specification, analysis and verification of service-oriented architectures and applications. We show how ADR is used as a formal ground for high-level modelling languages and approaches developed within Sensoria

04241 Abstracts Collection -- Graph Transformations and Process Algebras for Modeling Distributed and Mobile Systems

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. Processes in a communication network can be seen in two different ways: as terms in an algebraic theory, emphasizing their behaviour and their interaction with the environment, and as nodes (or edges) in a graph, emphasizing their topology and their connectedness. Especially topology, mobility and dynamic reconfigurations at runtime can be modelled in a very intuitive way using graph transformation. On the other hand the definition and proof of behavioural equivalences is often easier in the process algebra setting. Also standard techniques of algebraic semantics for universal constructions, refinement and compositionality can take better advantage of the process algebra representation. An important example where the combined theory is more convenient than both alternatives is for defining the concurrent (noninterleaving), abstract semantics of distributed systems. Here graph transformations lack abstraction and process algebras lack expressiveness. Another important example is the work on bigraphical reactive systems with the aim of deriving a labelled transitions system from an unlabelled reactive system such that the resulting bisimilarity is a congruence. Here, graphs seem to be a convenient framework, in which this theory can be stated and developed. So, although it is the central aim of both frameworks to model and reason about concurrent systems, the semantics of processes can have a very different flavour in these theories. Research in this area aims at combining the advantages of both frameworks and translating concepts of one theory into the other. The Dagsuthl Seminar, which took place from 06.06. to 11.06.2004, was aimed at bringing together researchers of the two communities in order to share their ideas and develop new concepts. These proceedings4 of the do not only contain abstracts of the talks given at the seminar, but also summaries of topics of central interest. We would like to thank all participants of the seminar for coming and sharing their ideas and everybody who has contributed to the proceedings

A coalgebraic semantics for causality in Petri nets

In this paper we revisit some pioneering efforts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and they can be fully explained as coalgebras on a presheaf category on an index category of partial orders. First, we provide a set-theoretic model in the form of a a causal case graph, that is a labeled transition system where states and transitions represent markings and firings of the net, respectively, and are equipped with causal information. Most importantly, each state has a poset representing causal dependencies among past events. Our first result shows the correspondence with behavior structure semantics as proposed by Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and have infinitely many states, but we show how they can be refined to get an equivalent finitely-branching model. In it, states are equipped with symmetries, which are essential for the existence of a minimal, often finite-state, model. The next step is constructing a coalgebraic model. We exploit the fact that events can be represented as names, and event generation as name generation. Thus we can apply the Fiore-Turi framework: we model causal relations as a suitable category of posets with action labels, and generation of new events with causal dependencies as an endofunctor on this category. Then we define a well-behaved category of coalgebras. Our coalgebraic model is still infinite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, which is equivalent to our set-theoretical compact model. Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin