PhD ThesisSynthesis 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.EPSR
