We present a theory of abstract interpretations in the framework of invariant sets by translating the notions of lattices and Galois connections into this framework, and presenting their properties in terms of finitely supported objects. We introduce the notions of invariant correctness relation and invariant representation function, emphasize an equivalence between them, and establish the relationship between these notions and invariant Galois connections. Finally, we provide some widening and narrowing techniques in order to approximate the least fixed points of finitely supported transition functions.

Summary In recent years, the use of accelerators in conjunction with CPUs, known as heterogeneous computing, has brought about significant performance increases for scientific applications. One of the best examples of this is lattice quantum chromodynamics (QCD), a stencil operation based simulation. These simulations have a large memory footprint necessitating the use of many graphics processing units (GPUs) in parallel. This requires the use of a heterogeneous cluster with one or more GPUs per node. In order to obtain optimal performance, it is necessary to determine an efficient communication pattern between GPUs on the same node and between nodes. In this paper, we present a performance model based method for minimizing the communication time of applications with stencil operations, such as lattice QCD, on heterogeneous computing systems with a non‐blocking InfiniBand interconnection network. The proposed method is able to increase the performance of the most computationally intensive kernel of lattice QCD by 25% due to improved overlapping of communication and computation. We also demonstrate that the aforementioned performance model and efficient communication patterns can be used to determine a cost efficient heterogeneous system design for stencil operation based applications. Copyright © 2014 John Wiley & Sons, Ltd.

We introduce and study the nominal groups, providing some algebraic properties of this new structure. We focus on the properties of nominal homomorphisms, and study the correspondence between some results obtained in the Fraenkel-Mostowski framework (where only finitely supported objects are allowed) and those obtained in the classical Zermelo-Fraenkel framework.