Geometry and Topology in Concurrency theory

Preliminary Proceedings of the Workshop on Geometry and Topology in Concurrency Theory

This presentation is the sequel of a paper published in GETCO'00 proceedings where a research program to construct an appropriate algebraic setting for the study of deformations of higher dimensional automata was sketched. This paper focuses precisely on detailing some of its aspects. The main idea is that the category of homotopy types can be embedded in a new category of dihomotopy types, the...

Algebraic topology and concurrency

1. Introduction This article is intended to provide some new insights about concurrency theory using ideas from geometry, and more speciically 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. ...

Preliminary Proceedings of the Workshop on Geometry and Topology in Concurrency Theory GETCO ’ 03 Marseille , France , September 6 , 2003

In this paper, we reason that simulation and bisimulation are not adequate in the context of hybrid systems as they are only capable of comparing states that are reachable in a finite number of transitions. To solve this problem we extend labelled transition systems with a topology on the state space. We define topological versions of simulation and bisimulation that are also capable of compari...

Concurrency and Directed Algebraic Topology

Arithmetic + Logic + Geometry = Concurrency

0 Introduction In deening concurrency one dichotomy that has arisen is between reductionism and primitivism. The reductionist viewpoint reduces concurrent behavior to nondeterministic sequential behavior by viewing it as interleaving. The primitive school treats concurrent behavior as a basic form of behavior in its own right, distinct from and indeed more general than sequential behavior. A ba...