## 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 by 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 [9] 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 computations. 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 [21] provide methods for doing this in the group case. The extension to monoids - ongoing collaborative work with Professor M. Johnson of Macquarie University, Sydney [23] - gives a general formalism for recording rewrites, thus providing checkable computation.
- 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 [22].
Please email Anne if you have an interest in joining the client group for testing Kan at a later stage. |

Author: *Anne Heyworth*

Last updated: 11th May 2001

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