*Result*: Automatic parallelisation for a class of URE problems

*This thesis deals with the methodology and software of automatic parallelisation for numerical supercomputing and supercomputers. Basically, we focus on the problem of Uniform Recurrence Equations (URE) which exists widely in numerical computations. vVepropose a complete methodology of automatic generation of parallel programs for regular array designs. The methodology starts with an introduction of a set of canonical dependencies which generates a general modelling of the various URE problems. Based on these canonical dependencies, partitioning and mapping methods are developed which gives the foundation of the universal design process. Using the theoretical results we propose the structures of parallel programs and eventually generate automatically parallel codes which run correctly and efficiently on transputer array. The achievements presented in this thesis can be regarded as a significant progress in the area of automatic generation of parallel codes and regular (systolic) array design. This methodology is integrated and self-contained, and may be the only practical working package in this area.*