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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 57 (4 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.
Detecting Deadlocks In Concurrent Systems
 IN CONCUR’98: CONCURRENCY THEORY (NICE
, 1998
"... We study deadlocks using geometric methods based on generalized process graphs [11], i.e., cubical complexes or HigherDimensional Automata (HDA) [23, 24, 30, 35], describing the semantics of the concurrent system of interest. A new algorithm is described and fully assessed, both theoretically a ..."
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Cited by 53 (12 self)
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We study deadlocks using geometric methods based on generalized process graphs [11], i.e., cubical complexes or HigherDimensional Automata (HDA) [23, 24, 30, 35], describing the semantics of the concurrent system of interest. A new algorithm is described and fully assessed, both theoretically and practically and compared with more wellknown traversing techniques. An implementation is
Hundreds of Impossibility Results for Distributed Computing
 Distributed Computing
, 2003
"... We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refe ..."
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Cited by 52 (5 self)
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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing.
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 50 (12 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...
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 ..."
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Cited by 33 (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
Higher Dimensional Automata Revisited
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2000
"... ..."
Transition and cancellation in concurrency and branching time
 Mathematical Structures in Computer Science 13(4) (2003
, 2002
"... We review the conceptual development of (true) concurrency and branching time starting from Petri nets and proceeding via Mazurkiewicz traces, pomsets, bisimulation, and event structures up to higher dimensional automata (HDAs), whose acyclic case may be identified with triadic event structures and ..."
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Cited by 15 (1 self)
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We review the conceptual development of (true) concurrency and branching time starting from Petri nets and proceeding via Mazurkiewicz traces, pomsets, bisimulation, and event structures up to higher dimensional automata (HDAs), whose acyclic case may be identified with triadic event structures and triadic Chu spaces. Acyclic HDAs may be understood as the extension of Boolean logic with a third truth value expressing transition. We prove the necessity of such a third value under mild assumptions about the nature of observable events, and show that the expansion of any complete Boolean basis L to L with a third literal �a expressing a = forms an expressively complete basis for the representation of acyclic HDAs. The main contribution is a new event state × of cancellation, sibling to, serving to distinguish a(b + c) from ab + ac while simplifying the extensional definitions of termination �A and sequence AB. We show that every HDAX (acyclic HDA with ×) is representable in the expansion of L to L × with a fourth literal �a expressing a = ×.
A Semantic View On Distributed Computability And Complexity
 In Proceedings of the 3rd Theory and Formal Methods Section Workshop. Imperial
, 1996
"... This paper intends to give a semantical perspective on the recent work by Herlihy, Shavit and Rajsbaum on computability and complexity results for tresilient and waitfree protocols for distributed systems. It is an extended abstract a of a talk given at the Imperial College Workshop, Oxford, Chr ..."
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Cited by 10 (3 self)
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This paper intends to give a semantical perspective on the recent work by Herlihy, Shavit and Rajsbaum on computability and complexity results for tresilient and waitfree protocols for distributed systems. It is an extended abstract a of a talk given at the Imperial College Workshop, Oxford, Christ Church on the 2nd of April 1996. 1 Introduction In this article we address some computability and complexity problems which have most often arisen in the area of protocols for distributed systems and concurrent databases. The essence of these problems is to decide whether we can compute a certain kind of function in a distributed  yet robust  manner. Let us take our first example from the concurrent database theory. Imagine that we have a database that can be shared by n concurrent transactions T 1 ; \Delta \Delta \Delta ; Tn asynchronously. We suppose that the network linking the transactions to the shared database is not reliable in the sense that any wire can be cut unexpectedly, ...
HOMOTOPICAL INTERPRETATION OF GLOBULAR COMPLEX BY MULTIPOINTED DSPACE
"... Abstract. Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CWcomplex. We prove that there exists a ..."
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Cited by 10 (4 self)
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Abstract. Globular complexes were introduced by E. Goubault and the author to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of the cellular decomposition of a CWcomplex. We prove that there exists a combinatorial model category such that the cellular objects are exactly the globular complexes and such that the homotopy category is equivalent to the homotopy category of flows. The underlying
Investigation of Concurrent Processes By Means of Homotopy Functors
, 1999
"... this paper . . . . . . . . . . . . . . . . . . . . . . . . . 4 ..."
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Cited by 9 (2 self)
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