Comparing Topological Models for Concurrency

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...

A Model Category for the Homotopy Theory of Concurrency

We construct a cofibrantly generated model structure on the category of flows such that any flow is fibrant and such that two cofibrant flows are homotopy equivalent for this model structure if and only if they are S-homotopy equivalent. This result provides an interpretation of the notion of S-homotopy equivalence in the framework of model categories. 1. Geometric models of concurrency Algebra...

Comparing Metabolic Pathways through Reactions and Potential Fluxes

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. ...

A Survey of Concurrency Control Algorithms in the Operating Systems

Concurrency control is one of the important problems in operation systems. Various studies have been reported to present different algorithms to address this problem, although a few attempts have been made to represent an overall view of the characteristics of these algorithms and comparison of their capabilities to each other. This paper presents a survey of the current methods for controlling...