Fabio Gadducci

A conceptual framework for adaptation

In this position paper we present a conceptual vision of adaptation, a key feature of autonomic systems. We put some stress on the role of control data and argue how some of the programming paradigms and models used for adaptive systems match with our conceptual framework.

An Algebraic Presentation of Term Graphs, via GS-Monoidal Categories

We present a categorical characterization of term graphs (i.e., finite, directed acyclic graphs labeled over a signature) that parallels the well-known characterization of terms as arrows of the algebraic theory of a given signature (i.e., the free Cartesian category generated by it). In particular, we show that term graphs over a signature Σ are one-to-one with the arrows of the free gs-monoidal category generated by Σ. Such a category satisfies all the axioms for Cartesian categories but for the naturality of two transformations (the discharger ! and the duplicator ∇), providing in this way an abstract and clear relationship between terms and term graphs. In particular, the absence of the naturality of ∇ and ! has a precise interpretation in terms of explicit sharing and of loss of implicit garbage collection, respectively.

An inductive view of graph transformation

The dynamic behavior of rule-based systems (like termrewriting systems [24], process algebras [27], and so on) can be traditionally determined in two orthogonal ways. Either operationally, in the sense that a way of embedding a rule into a state is devised, stating explicitly how the result is built: This is the role played by (the application of) a substitution in term rewriting. Or inductively, showing how to build the class of all possible reductions from a set of basic ones: For term rewriting, this is the usual definition of the rewrite relation as the minimal closure of the rewrite rules. As far as graph transformation is concerned, the operational view is by far more popular: In this paper we lay the basis for the orthogonal view. We first provide an inductive description for graphs as arrows of a freely generated dgs-monoidal category. We then apply 2-categorical techniques, already known for term and term graph rewriting [29, 7], recasting in this framework the usual description of graph transformation via double-pushout [13].

About permutation algebras, (pre)sheaves and named sets

In this paper we survey some well-known approaches proposed as general models for calculi dealing with names (like for example process calculi with name-passing). We focus on (pre)sheaf categories, nominal sets, permutation algebras and named sets, studying the relationships among these models, thus allowing techniques and constructions to be transferred from one model to the other.

A 2-Categorical Presentation of Term Graph Rewriting

It is well-known that a term rewriting system can be faithfully described by a cartesian 2-category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2-categorical presentation for term graph rewriting. Building on a result presented in [8], which shows that term graphs over a given signature are in one-to-one correspondence with arrows of a gs-monoidal category freely generated from the signature, we associate with a term graph rewriting system a gs-monoidal 2-category, and show that cells faithfully represent its rewriting sequences. We exploit the categorical framework to relate term graph rewriting and term rewriting, since gs-monoidal (2-)categories can be regarded as “weak” cartesian (2-) categories, where certain (2-)naturality axioms have been dropped.

A bi-categorical axiomatisation of concurrent graph rewriting

Abstract In this paper the concurrent semantics of double-pushout (DPO) graph rewriting, which is classically defined in terms of shift-equivalence classes of graph derivations, is axiomatised via the construction of a free monoidal bi-category. In contrast to a previous attempt based on 2-categories, the use of bi-categories allows to define rewriting on concrete graphs. Thus, the problem of composition of isomorphism classes of rewriting sequences is avoided. Moreover, as a first step towards the recovery of the full expressive power of the formalism via a purely algebraic description, the concept of disconnected rules is introduced, i.e., rules whose interface graphs are made of disconnected nodes and edges only. It is proved that, under reasonable assumptions, rewriting via disconnected rules enjoys similar concurrency properties like in the classical approach.

A behavioural congruence for web services

Web services are emerging as a promising technology for the development of next generation distributed heterogeneous software systems. We define a new behavioural equivalence for Web services, based on bisimilarity and inspired by recent advances in the theory of reactive systems. The proposed equivalence is compositional and decidable, and it provides a firm ground for enhanced behaviour-aware discovery and for a sound incremental development of services and service compositions.

Reactive Systems, Barbed Semantics, and the Mobile Ambients

Reactive systems, proposed by Leifer and Milner, represent a meta-framework aimed at deriving behavioral congruences for those specification formalisms whose operational semantics is provided by rewriting rules. Despite its applicability, reactive systems suffered so far from two main drawbacks. First of all, no technique was found for recovering a set of inference rules, e.g. in the so-called SOS style, for describing the distilled observational semantics. Most importantly, the efforts focused on strong bisimilarity, tackling neither weak nor barbed semantics. Our paper addresses both issues, instantiating them on a calculus whose semantics is still in a flux: Cardelli and Gordons mobile ambients. While the solution to the first issue is tailored over our case study, we provide a general framework for recasting (weak) barbed equivalence in the reactive systems formalism. Moreover, we prove that our proposal captures the behavioural semantics for mobile ambients proposed by Rathke and Sobocinski and by Merro and Zappa Nardelli.

Comparing logics for rewriting

The large diffusion of concurrent and distributed systems has spawned in recent years a variety of new formalisms, equipped with features for supporting an easy specification of such systems. The aim of our paper is to analyze three proposals, namely rewriting logic, action calculi and tile logic, chosen among those formalisms designed for the description of rule-based systems. For each of these logics we first try to understand their foundations, then we briefly sketch some applications. The overall goal of our work is to find out a common layout where these logics can be recast, thus allowing for a comparison and an evaluation of their specific features.

A concurrent graph semantics for Mobile Ambients

Abstract We present an encoding for finite processes of the mobile ambients calculus into term graphs, proving its soundness and completeness with respect to the original, interleaving operational semantics. With respect to most of the other approaches for the graphical implementation of calculi with name mobility, our term graphs are unstructured (that is, non hierarchical), thus avoiding any “encapsulation” of processes. The implication is twofold. First of all, it allows for the reuse of standard graph rewriting theory and tools for simulating the reduction semantics. More importantly, it allows for the simultaneous execution of independent reductions, which are nested inside ambients, thus offering a concurrent semantics for the calculus.