Richard K. Squier

Computing with solitons: a review and prospectus

We review work on computing with solitons, from the discovery of solitons in cellular automata, to an abstract model for particle computation, to information transfer in collisions of optical solitons, to state transformations in collisions of vector soli-tons. We conclude by discussing open problems and the prospects for practical applications using optical solitons in photo-refractive crystals and other materials.

Implementation of parallel arithmetic in a cellular automaton

We describe an approach to parallel computation using particle propagation and collisions in a one-dimensional cellular automaton using a Particle model-a Particle Machine (PM). Such a machine has the parallelism, structural regularity, and local connectivity of systolic arrays, but is general and programmable. It contains no explicit multipliers, adders, or other fixed arithmetic operations; these are implemented using fine-grain interactions of logical particles which are injected into the medium of the cellular automaton, and which represent both data and processors. We give parallel, linear-time implementations of addition, subtraction, multiplication and division.

The number of edges in a subgraph of a Hamming graph

Abstract Let G be a subgraph of the Cartesian product Hamming graph (Kp)r with n vertices. Then the number of edges of G is at most ( 1 2 )(p − 1) logp n, with equality holding if and only G is isomorphic to (Kp)s for some s ≤ r.

Computing with Classical Soliton Collisions

We review work on computing with solitons, from the discovery of solitons in cellular automata, to an abstract model for particle computation, information transfer in collisions of optical solitons, state transformations in collisions of vector solitons, a proof of the universality of blinking spatial solitons, and the demonstration of multistable collision cycles and their application to state-restoring logic. We conclude by discussing open problems and the prospects for practical computing applications using optical soliton collisions in photo-refractive crystals and fibers.

Comparing architectures using throughput-versus-cost modeling

The paper compares two parallel architectures in terms of throughput versus cost. Throughput is estimated using machine parameters extracted from detailed models of each architecture. Cost models are used to express total resource use in terms of a common unit. Performance of an architecture is then evaluated by optimizing throughput for each possible cost. Finally, these throughput-versus-cost results for the two architectures are compared for a particular class of problems: iterative computations on a 2-dimensional grid. The results show that there is a cost below which one architecture is an order of magnitude faster than the other, and above which this relationship is reversed. This approach may prove useful as a general comparison methodology.<<ETX>>

A Comparison of Two Application-Specific Architectures for 2-d Mesh Computations

This paper considers the question of whether a mesh-connected machine is always better than a multi-pipelined machine for iterative 2-d mesh computations. Optimal throughput is determined as a function of a unified measure of resources (cost). The resulting performance curves for the two architectures show that there is a cost below which the pipelined architecture is an order of magnitude faster than the mesh, and above which this relationship is reversed. This methodology of comparing architectures using throughput-versus-cost modeling may prove useful in other contexts.