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Relations in Concurrency
"... 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 seman ..."
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Cited by 263 (33 self)
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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 higherorder 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 higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
SOME GEOMETRIC PERSPECTIVES IN CONCURRENCY THEORY
 HOMOLOGY, HOMOTOPY AND APPLICATIONS, VOL.5(2), 2003, PP.95–136
, 2003
"... Concurrency, i.e., the domain in computer science which deals with parallel (asynchronous) computations, has very strong links with algebraic topology; this is what we are developing in this paper, giving a survey of “geometric” models for concurrency. We show that the properties we want to prove on ..."
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Cited by 43 (3 self)
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Concurrency, i.e., the domain in computer science which deals with parallel (asynchronous) computations, has very strong links with algebraic topology; this is what we are developing in this paper, giving a survey of “geometric” models for concurrency. We show that the properties we want to prove on concurrent systems are stable under some form of deformation, which is almost homotopy. In fact, as the “direction ” of time matters, we have to allow deformation only as long as we do not reverse the direction of time. This calls for a new homotopy theory: “directed ” or dihomotopy. We develop some of the geometric intuition behind this theory and give some hints about the algebraic objects one can associate with it (in particular homology groups). For some historic as well as for some deeper reasons, the theory is at a stage where there is a nice blend between cubical, ωcategorical and topological techniques.
Petri Nets And Step Transition Systems
 International Journal of Foundations of Computer Science
, 1992
"... Labelled transition systems are a simple yet powerful formalism for describing the operational behaviour of computing systems. They can be extended to model concurrency faithfully by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step. Petri ne ..."
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Cited by 43 (1 self)
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Labelled transition systems are a simple yet powerful formalism for describing the operational behaviour of computing systems. They can be extended to model concurrency faithfully by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step. Petri nets (or Place/Transition nets) give rise to such step transition systems in a natural way  the marking diagram of a Petri net is the canonical transition system associated with it. In this paper, we characterize the class of PNtransition systems, which are precisely those step transition systems generated by Petri nets. We express the correspondence between PNtransition systems and Petri nets in terms of an adjunction between a category of PNtransition systems and a category of Petri nets in which the associated morphisms are behaviourpreserving in a strong and natural sense.
Algebraic Topology And Concurrency
 Theoretical Computer Science
, 1998
"... This article is intended to provide some new insights about concurrency theory using ideas from geometry, and more specifically from algebraic topology. The aim of the paper is twofold: we justify applications of geometrical methods in concurrency through some chosen examples and we give the mathem ..."
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Cited by 40 (8 self)
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This article is intended to provide some new insights about concurrency theory using ideas from geometry, and more specifically from algebraic topology. The aim of the paper is twofold: we justify applications of geometrical methods in concurrency through some chosen examples and we give the mathematical foundations needed to understand the geometric phenomenon that we identify. In particular we show that the usual notion of homotopy has to be refined to take into account some partial ordering describing the way time goes. This gives rise to some new interesting mathematical problems as well as give some common grounds to computerscientific problems that have not been precisely related otherwise in the past. The organization of the paper is as follows. In Section 2 we explain to which extent we can use some geometrical ideas in computer science: we list a few of the potential or well known areas of application and try to exemplify some of the properties of concurrent (and distributed) systems we are interested in. We first explain the interest of using some geometric ideas for semantical reasons. Then we take the example of concurrent databases with the problem of finding deadlocks and with some aspects of serializability theory. More general questions about schedules can be asked as well and related to some geometric considerations, even for scheduling microinstructions (and not only coarsegrained transactions as for databases). The final example is the one of faulttolerant protocols for distributed systems, where subtle scheduling properties go into play. In Section 3 we give the first few definitions needed for modeling the topological spaces arising from Section 2. Basically, we need to define a topological space containing all traces of executions of the concu...
Hereditary History Preserving Bisimulations or What is the Power of the Future Perfect in Program Logics
 Polish Academy of Sciences
, 1991
"... Contents 1 History Preserving Bisimulations on Labelled Event Structures 2 1.1 Finitary Prime Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Labelled Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 History Preserving Bisimulations ..."
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Cited by 36 (0 self)
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Contents 1 History Preserving Bisimulations on Labelled Event Structures 2 1.1 Finitary Prime Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Labelled Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 History Preserving Bisimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Relations Between History Preserving Bisimulations . . . . . . . . . . . . . . . . 5 2 History Preserving Bisimulations and Refinement 7 2.1 Refinement of Labelled Event Structures . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 History Preserving Bisimulations vs Refinement . . . . . . . . . . . . . . . . . . . 8 3 Back and Forth Bisimulation on Sequential Systems 8 3.1 Unfolding transition systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Unfolding versus BackandForth Bisimulation . . . . . . . . . . . . . . . . . . . 12 3.3 The Power of the Future Pe
Geometry and Concurrency: A User's Guide
, 2000
"... Introduction "Geometry and Concurrency" is not yet a wellestablished domain of research, but is rather made of a collection of seemingly related techniques, algorithms and formalizations, coming from different application areas, accumulated over a long period of time. There is currently a certain ..."
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Cited by 29 (7 self)
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Introduction "Geometry and Concurrency" is not yet a wellestablished domain of research, but is rather made of a collection of seemingly related techniques, algorithms and formalizations, coming from different application areas, accumulated over a long period of time. There is currently a certain amount of effort made for unifying these (in particular see the article (Gunawardena, 1994)), following the workshop "New Connections between Computer Science and Mathematics" held at the Newton Institute in Cambridge, England in November 1995 (and sponsored by HP/BRIMS). More recently, the first workshop on the very same subject has been held in Aalborg, Denmark (see http://www.math.auc.dk/~raussen/admin/workshop/workshop.html where the articles of this issue, among others, have been first sketched. But what is "Geometry and Concurrency" composed of then? It is an area of research made of techniques which use geometrical reasoning for describing and solving problems
A Logical Study of Distributed Transition Systems
, 1995
"... We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an actionbased temporal logic in which one can explicitly talk about steps. The log ..."
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Cited by 29 (5 self)
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We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an actionbased temporal logic in which one can explicitly talk about steps. The logic is studied to establish a variety of positive and negative results in terms of axiomatizability and decidability. Our positive results show that the step notion is amenable to logical treatment via standard techniques. They also help us to obtain a logical characterization of two well known models for distributed systems: labelled elementary net systems and labelled prime event structures. Our negative results show that demanding deterministic structures when dealing with a "noninterleaved " notion of transitions is, from a logical standpoint, very expressive. They also show that another well known model of distributed systems called asynchronous transition systems exhibits a surprising a...
Timing and Causality in Process Algebra
 Acta Informatica
, 1992
"... . There has been considerable controversy in concurrency theory between the `interleaving' and `true concurrency' schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences; the latter adopts more comple ..."
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Cited by 27 (0 self)
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. There has been considerable controversy in concurrency theory between the `interleaving' and `true concurrency' schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences; the latter adopts more complex semantic structures to avoid reducing concurrency to interleaving. In this paper we show that the two approaches are not irreconcilable. We define a timed process algebra where occurrences are associated with intervals of time, and give it a transition system semantics. This semantics has many of the advantages of the interleaving approach; the algebra admits an expansion theorem, and bisimulation semantics can be used as usual. Our transition systems, however, incorporate timing information, and this enables us to express concurrency: merely adding timing appropriately generalises transition systems to asynchronous transition systems, showing that time gives a link between true concurrenc...
Models for NamePassing Processes: Interleaving and Causal
 In Proceedings of LICS 2000: the 15th IEEE Symposium on Logic in Computer Science (Santa Barbara
, 2000
"... We study syntaxfree models for namepassing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual picalculus operations, defining Indexed Labelled Transition Systems. For noninterleaving causal semantics we de ..."
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Cited by 24 (3 self)
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We study syntaxfree models for namepassing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual picalculus operations, defining Indexed Labelled Transition Systems. For noninterleaving causal semantics we define Indexed Labelled Asynchronous Transition Systems, smoothly generalizing both our interleaving model and the standard Asynchronous Transition Systems model for CCSlike calculi. In each case we relate a denotational semantics to an operational view, for bisimulation and causal bisimulation respectively. We establish completeness properties of, and adjunctions between, categories of the two models. Alternative indexing structures and possible applications are also discussed. These are first steps towards a uniform understanding of the semantics and operations of namepassing calculi.
Firstorder axioms for asynchrony
 In Proc. CONCUR
, 1997
"... Abstract. We study properties of asynchronous communication independently of any concrete concurrent process paradigm. We give a generalpurpose, mathematically rigorous definition of several notions of asynchrony in a natural setting where an agent is asynchronous if its input and/or output is filt ..."
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Cited by 23 (2 self)
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Abstract. We study properties of asynchronous communication independently of any concrete concurrent process paradigm. We give a generalpurpose, mathematically rigorous definition of several notions of asynchrony in a natural setting where an agent is asynchronous if its input and/or output is filtered through a buffer or a queue, possibly with feedback. In a series of theorems, we give necessary and sufficient conditions for each of these notions in the form of simple firstorder or secondorder axioms. We illustrate the formalism by applying it to asynchronous CCS and the core join calculus.