On the synthesis of integral and dynamic recurrences
Synthesis techniques for regular arrays provide a disciplined and well-founded approach to the design of classes of parallel algorithms. The design process is guided by a methodology which is based upon a formal notation and transformations. The mathematical model underlying synthesis techniques is that of affine Euclidean geometry with embedded lattice spaces. Because of this model, computationally powerful methods are provided as an effective way of engineering regular arrays. However, at present the applicability of such methods is limited to so-called affine problems. The work presented in this thesis aims at widening the applicability of standard synthesis methods to more general classes of problems. The major contributions of this thesis are the characterisation of classes of integral and dynamic problems, and the provision of techniques for their systematic treatment within the framework of established synthesis methods. The basic idea is the transformation of the initial algorithm specification into a specification with data dependencies of increased regularity, so that corresponding regular arrays can be obtained by a direct application of the standard mapping techniques. We will complement the formal development of the techniques with the illustration of a number of case studies from the literature.