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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.
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 52 (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 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
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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this paper . . . . . . . . . . . . . . . . . . . . . . . . . 4
Point Glueing in CpoS
, 1998
"... Point glueing in cpos This report explains how to factor partial orders to get quotient partial orders and how to factor cpos to get quotient cpos. This is supplemented by an important issue of collapsing the cpos to simpler ones. The motivations for this research come from investigations of co ..."
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Cited by 4 (2 self)
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Point glueing in cpos This report explains how to factor partial orders to get quotient partial orders and how to factor cpos to get quotient cpos. This is supplemented by an important issue of collapsing the cpos to simpler ones. The motivations for this research come from investigations of concurrent processes addressed elsewhere. However, the article may be read independently of these motivations. Streszczenie Sklejanie punkto'oow w cpotach W tej pracy wyja'sniam jak dzielic'cc porzaa ' adki czee ' e'sciowe przez relacje ro'oownowazno'sci, zeby otrzymac'cc porzaa ' adki czee ' e'sciowe oraz jak dzielic'cc zupe/lne /la'ncuchowo porzaa ' adki czee ' e'sciowe (cpoty) przez relacje ro'oownowazno'sci, zeby otrzymac'cc cpoty. Dalej omawiam wazne zagadnienie kolapsowania cpoto'oow do prostszej postaci. Motywacje pochodzaa ' a z omawianych gdzie indziej bada'n proceso'oow wspo'oo/lbieznych. Jednak niniejszy artyku/l mozna czytac'cc niezaleznie od tych motywacji. Contents 0 ...
Point glueing in cpos \Lambda
, 1998
"... \Lambda Partially supported by LoSSeD workpackage within the CRIT2 project funded by ESPRIT and INCO programmes. Report available electronically at ftp:==ftp.ipipan.gda.pl=stefan=reports = 60partordglue.ps.gz. ..."
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\Lambda Partially supported by LoSSeD workpackage within the CRIT2 project funded by ESPRIT and INCO programmes. Report available electronically at ftp:==ftp.ipipan.gda.pl=stefan=reports = 60partordglue.ps.gz.