A Grid-based Application of Machine Learning to Model Generation

The classification of mathematical structures is a driving force in pure mathematics. A first step in producing algebraic classification theorems is to determine for which sizes certain algebras exist. Computational approaches to solving such existence problems using constraint satisfaction and model generation approaches have had much success. We look here at the question of distributing the model generation process using Grid technology. We present a novel distribution approach which involves using the HR machine learning program to intelligently suggest specialisations of the problem which are given to separate processors. Using the MACE, FINDER and SEM model generators, we demonstrate how this approach provides greater efficiency over a single-process approach for a series of quasigroup existence problems. We compare several approaches for the production and choice of specialisations, including the generation of proved classification theorems for algebraic structures of small sizes. We discuss how this approach could be used for more general problems.