The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higher-order processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higher-order processes. For this it is useful to generalise event structures to allow events which “persist.”

This paper combines and extends the material of [GG-a/c/d/e], except for the part in [GG-c] on refinement of transitions in Petri nets and the discussion of TCSP-like parallel composition in [GG-e]. An informal presentation of some basic ingredients of this paper appeared as [GG-b]. Among others, the treatment of action refinement in stable and non-stable event structures is new. The research reported here was supported by Esprit project 432 (METEOR), Esprit Basic Research Action 3148 (DEMON), Sonderforschungsbereich 342 of the TU Munchen, ONR grant N00014-92-J-1974 and the Human Capital and Mobility Cooperation Network EXPRESS (Expressiveness of Languages for Concurrency). Contents

We investigate the difference between two well-known notions of independence bisimilarity, history-preserving bisimulation and hereditary history-preserving bisimulation. We characterise the difference between the two bisimulations in trace-theoretical terms, advocating the view that the first is (just) a bisimulation for causality, while the second is a bisimulation for concurrency. We explore the frontier zone between the two notions by defining a hierarchy of bounded backtracking bisimulations.

s are available from the same host in the directory /pub/TR/UBLCS/ABSTRACTS in plain text format. All local authors can be reached via e-mail at the address last-name@cs.unibo.it. UBLCS Technical Report Series 93-15 Data Algorithm: A Numerical Method to Extract Shape Information from Gray Scale Images, R. Davoli, F. Tamburini, June 1993. 93-16 Towards Performance Evaluation in Process Algebras, R. Gorrieri, M. Roccetti, July 1993. 93-17 Split and ST Bisimulation Semantics, R. Gorrieri, C. Laneve, July 1993. 93-18 Multilanguage Interoperability, G. Attardi, M. Gaspari, July 1993. 93-19 HERMES: an Expert System for the Prognosis of Hepatic Diseases, I. Bonf a, C. Maioli, F. Sarti, G.L. Milandri, P.R. Dal Monte, September 1993. 93-20 An Information Flow Security Property for CCS, R. Focardi, R. Gorrieri, October 1993. 93-21 A Classification of Security Properties, R. Focardi, R. Gorrieri, October 1993. 93-22 Real Time Systems: A Tutorial, F. Panzieri, R. Davoli, October 1993. 93-23 A Sca...

In this paper the notion of action atomicity is relaxed by permitting actions to be observed in the middle of their evolution. Non atomic semantic equivalences, based on the notion of bisimulation, are studied over stable event structures. Splitn bisimulation equivalence (denoted n ¸) considers each event as composed of n phases. ST bisimulation equivalence (denoted ST ¸ ) is a slight refinement of 2 ¸ where each ending phase is unambiguously associated to a beginning phase. We prove that, by increasing n, we get finer and finer equivalences (i.e. n+1 ¸ ` n ¸) and, moreover, that n+1 ¸ coincides with ST ¸ over those event structures whose autoconcurrency is at most n. The main consequence of these results is that, for image finite event structures, ST ¸ is the intersection of all the n ¸. 1 Introduction Most of the behavioural equivalences for concurrent systems are usually based on the assumption that the execution of an action is an atomic activity which cannot b...

This paper appeared as Arbeitspapiere der GMD 594, Sankt Augustin 1991. The work presented here has partly been carried out within the Esprit Basic Research Action 3148 (DEMON) and the Sonderforschungsbereich 182 of the University of ErlangenN urnberg. 1 Introduction

The formal step by step development of implementations from specifications is necessary to allow the incremental description of large software systems and hence split the software development process in manageable portions. Due to the complex notion of objects as units of structure and behavior, the refinement process has to be reconsidered in the object-oriented framework. Apart from refining structure the behavioral part gives rise to refine actions by transactions. Referring to information systems as application domain, concurrency control aspects come into play because of shared resources. We present an approach to incorporate transactions into object-oriented specification and illustrate the main problems of synchronizing them on commonly used resources.

This paper extends to process algebras the notion of maximality which has initially been introduced for prime event structures and P/T nets and shows how this notion of maximality may be used for defining an adequate semantics of Basic LOTOS able to support action refinement. Such an approach appears to be more convenient than the classical STsemantics where non atomic actions are split into start and end sub-actions, as it makes it possible to escape from the potential state space explosion problems induced by action splitting. Main contributions of the paper are related to the definition of a maximality-based operational semantics of LOTOS and to the expression of maximality-based bisimulation equivalences which are shown to be preserved under action refinement.

We propose a framework for the specification of behaviourpreserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimitbased composition operation. We show that natural notions of (strong and weak) bisimilarity over open nets are congruences with respect to the composition operation. We also provide an up-to technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the double-pushout approach to rewriting) whose application preserves the observational semantics of the net.

This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing their behaviour in a mathematical model. For concurrent systems the interesting aspect of their computation is often how they interact with the environment during a computation and not in which state they terminate, indeed they may not be intended to terminate at all. For this reason they are often referred to as reactive systems, to distinguish them from traditional calculational systems, as e.g. a program calculating your income tax, for which the interesting behaviour is the answer it gives when (or if) it terminates, in other words the (possibly partial) function it computes between input and output. Church's thesis tells us that regardless of whether we choose the lambda calculus, Turing machines, or almost any modern programming language such as C or Java to describe calculational systems, we are able to describe exactly the same class of functions. However, there is no agreement on observable behaviour for concurrent reactive systems, and consequently there is no correspondent to Church's thesis. A result of this fact is that an overwhelming number of di#erent and often competing notions of observable behaviours, primitive operations, languages and mathematical models for describing their semantics, have been proposed in the litterature on concurrency.