P = FS: Parallel is Just Fast Serial

TL;DR

This paper proves that parallel processing with identical processors is equivalent to fast serial processing, providing new insights into applying parallelism and extending the theorem to heterogeneous arrays.

Contribution

It introduces a novel theorem establishing the equivalence between homogeneous parallel and fast serial processing, and extends this to optimize heterogeneous array latency.

Findings

Homogeneous parallel processing is equivalent to fast serial processing.

The theorem helps identify new opportunities for parallelism.

Extension to heterogeneous arrays improves latency optimization.

Abstract

We prove that parallel processing with homogeneous processors is logically equivalent to fast serial processing. The reverse proposition can also be used to identify obscure opportunities for applying parallelism. To our knowledge, this theorem has not been previously reported in the queueing theory literature. A plausible explanation is offered for why this might be. The basic homogeneous theorem is also extended to optimizing the latency of heterogenous parallel arrays.