Clients for Kan
- Professor J. Berrick of the National University of Singapore is
interested in classifying knots by comparing the quandles or left and
right cancellative monoids associated to them. These structures are given
finite presentations similar to those for which we already
use rewriting, therefore we expect that an applicable rewriting
technique can be developed.
- Dr A. Chandler and Dr L. Blair at the University of
Lancaster model dynamic and concurrent systems using Petri nets and
consequently need tools to determine properties such as
reachability, reversibility, boundedness and liveness. Preliminary
collaborations have successfully applied some rewriting techniques
to modelling navigation systems of mobile
robots  and indicate that further research should result
in tools for more general Petri net analysis.
- Dr B. Westbury at the University of Warwick wishes to
calculate the dimensions of certain finitely presented algebras. The
prototype of Kan could do this in theory but the
implementation proved to be too inefficient. We have identified
specific measures to improve the general flexibility and efficiency
of the program which should allow it to achieve the required
Possible extensions discussed with Dr Westbury would
be in the area of tensor algebra.
- Professor R. Brown and Dr C. D. Wensley of the University of
Wales, Bangor want to calculate homotopical and
(co)homological properties of monoids and groups from their presentations
[5,12] by constructing
a higher dimensional version of a resolution [10,43].
Logged rewriting techniques  provide
methods for doing this in the group case. The
extension to monoids - ongoing collaborative work with Professor
M. Johnson of Macquarie University, Sydney  - gives a
general formalism for recording rewrites, thus providing checkable
- Dr J. Snellman, at the University of Linköping, Sweden is
interested in constructing and investigating ``generic forms in
infinitely many variables'' which are a key area in the theory of
polynomial rings. He has informed us that the proposed Kan package
would be able to tackle problems of this type and this has initiated
an (ongoing) collaboration aimed at verifying this fact .
Please email Anne if you
have an interest in joining the client group for testing Kan at a later stage.
Background to Kan.
Detailed description of Kan.
The prototype of Kan.
Back to Anne's home page.
Author: Anne Heyworth
Last updated: 11th May 2001
MCS Web Maintainer
Any opinions expressed on this page are those of the author.
© University of Leicester.