CASE for concurrent systems based on the computer algebra of n-categories
Date: July 18th (Thursday)
Time: 14:45-15:05
Abstract
Richard Buckland will describe a concrete application of computational category
theory in which a system designed to perform computations in n-categories is used as the
engine for a computer assisted software engineering (CASE) tool for concurrent systems.
The skeletal structure of higher dimensional categories has been found to provide a useful
model of concurrent computation. However calculating with such higher dimensional
algebraic objects is, as is well known to those who have done such calculations, surprisingly
difficult. This difficulty arises both from the combinatorial complexity of all but the most
trivial or low dimensional examples, and from the problem of verifying the reasonableness
of procedures or results since we have little native intuition when dealing with high
dimensions. To assist in this difficult task of high dimensional calculation a computational
system has been developed to perform calculations with Schemes (schemes are the skeletal
structures underlying paths in omega categories).
This talk will briefly describe the algorithms for calculating with Schemes and will then
show how, in a nice piece of circularity, this computer-aided mathematics has as an
application the engine of a CASE tool to specify computational systems.
