Specification and Verification of a Wavefront Algorithm for the Algebraic Path Problem

In a seminal paper [1], Kung et al proposed that wavefront computation could be used to specify and implement parallel algorithms for the mathematical computations needed for highperformance signal processing. In [1], a wavefront computation is regarded as executing in a data-driven fashion on a two-dimensional grid of computational cells that have a north-southeast-west interconnection network. Computations start in the upper left corner of the grid and proceed diagonally toward the lower right corner. The arrival of the data in a wavefront at a cell triggers the computation in that cell, which in turn generates the data needed to propagate the wavefront. Rice and Seidman [3] propose a generalized model of wavefront computation based on an interconnection network that is an n-dimensional array of cells and also introduce syntax and semantics for a wavefront language. Rice has recently [2] used methods and ideas from group theory and topology to extend the wavefront model to a broad class of interconnection networks. In this paper, the semantics for the Rice-Seidman n-dimensional wavefront language will be discussed in the context of Rice ́s general model of wavefront computation. The semantics will then be used to give a formal verification of a wavefront algorithm for the algebraic path problem.