Characterizing Behavioural Congruences for Petri Nets

We exploit a notion of interface for Petri nets in order to design a set of net combinators. For such a calculus of nets, we focus on the behavioural congruences arising from four simple notions of behaviour, viz., traces, maximal traces, step, and maximal step traces, and from the corresponding four notions of bisimulation, viz., weak and weak step bisimulation and their maximal versions. We characterize such congruences via universal contexts and via games, providing in such a way an understanding of their discerning powers

Higher Dimensional Transition Systems

We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover, we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures

A convenient category of locally preordered spaces

As a practical foundation for a homotopy theory of abstract spacetime, we extend a category of certain compact partially ordered spaces to a convenient category of locally preordered spaces. In particular, we show that our new category is Cartesian closed and that the forgetful functor to the category of compactly generated spaces creates all limits and colimits.Comment: 26 pages, 0 figures, partially presented at GETCO 2005; changes: claim of Prop. 5.11 weakened to finite case and proof changed due to problems with proof of Lemma 3.26, now removed; Eg. 2.7, statement before Lem. 2.11, typos, and other minor problems corrected throughout; extensive rewording; proof of Lem. 3.31, now 3.30, adde

An interactive semantics of logic programming

We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational machinery of such a programming paradigm. The semantic framework we have chosen for presenting our results is tile logic, which has the advantage of allowing a uniform treatment of goals and observations and of applying abstract categorical tools for proving the results. As main contributions, we mention the finitary presentation of abstract unification, and a concurrent and coordinated abstract semantics consistent with the most common semantics of logic programming. Moreover, the compositionality of the tile semantics is guaranteed by standard results, as it reduces to check that the tile systems associated to logic programs enjoy the tile decomposition property. An extension of the approach for handling constraint systems is also discussed.Comment: 42 pages, 24 figure, 3 tables, to appear in the CUP journal of Theory and Practice of Logic Programmin

Petri Nets and Other Models of Concurrency

This paper retraces, collects, and summarises contributions of the authors --- in collaboration with others --- on the theme of Petri nets and their categorical relationships to other models of concurrency

Modular Composition of Language Features through Extensions of Semantic Language Models

Today, programming or specification languages are often extended in order to customize them for a particular application domain or to refine the language definition. The extension of a semantic model is often at the centre of such an extension. We will present a framework for linking basic and extended models. The example which we are going to use is the RSL concurrency model. The RAISE specification language RSL is a formal wide-spectrum specification language which integrates different features, such as state-basedness, concurrency and modules. The concurrency features of RSL are based on a refinement of a classical denotational model for process algebras. A modification was necessary to integrate state-based features into the basic model in order to meet requirements in the design of RSL. We will investigate this integration, formalising the relationship between the basic model and the adapted version in a rigorous way. The result will be a modular composition of the basic process model and new language features, such as state-based features or input/output. We will show general mechanisms for integration of new features into a language by extending language models in a structured, modular way. In particular, we will concentrate on the preservation of properties of the basic model in these extensions