Sheaf tools for computation
type: Item
instance of: scholarly article
title: Sheaf tools for computation
zbMATH Open document ID: 1130.18007
author: Elena Şendroiu
published in: Applied Mathematics and Computation
publication date: 2007-03-12T00:00:00Z
review text: The paper presents first how we can compute sheaf tools for accomplishing our goal, i.e., an authentication method by sheaves. The authors use the most general notion of a sheaf, as a functor on a site, which is a category equipped with a Grothendieck topology. Moreover, they have introduced a notion in sheaf theory, family for matching, in order to simplify the sheaf definition in a computation class of sites called well structured sites. This has given them the possibility to construct an optimal validation algorithm of sheaves. Also, they present an algorithm to generate sheaves. By handling the concepts of Goguen, the behaviour of a system is computed in the internal language of a (pre)sheaf topos. Non-interference by Goguen is also computed in the internal language of a presheaf topos by using predicates. Consequently, this paper provides computation tools for authentication and for non-interference control. In particular, the authors see that all computation tools are building from the base category that is provided by the architecture of distributed computing systems. It remains for them to try these out. Only, a software built in accordance with the ideas of this paper can provide real examples. The authors plan to implement this in the future.
reviewed by: Jesús Medina Moreno
Mathematics Subject Classification ID: 18F20
Mathematics Subject Classification ID: 18A05
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 18A15
Mathematics Subject Classification ID: 18F10
Mathematics Subject Classification ID: 68Q85
zbMATH DE Number: 5132891
zbMATH Keywords: category theory
zbMATH Keywords: topos theory
zbMATH Keywords: presheaves
zbMATH Keywords: sieves
zbMATH Keywords: site
zbMATH Keywords: sheaves
zbMATH Keywords: well structured site
zbMATH Keywords: authentication
zbMATH Keywords: non-interference
MaRDI profile type: Publication
full work available at URL: j.amc.2005.12.069
OpenAlex ID: W2075993739
cites work: Sheaf semantics for concurrent interacting objects
cites work: Q4040149
cites work: Sheaves in geometry and logic: a first introduction to topos theory
cites work: On the role of description
DOI: 10.1016/J.AMC.2005.12.069
description: scientific article; zbMATH DE number 5132891