A unifying approach to software and hardware design for scientific calculations and idempotent mathematics

TL;DR

The paper proposes idempotent analysis as a unifying framework for scientific computation, replacing conventional arithmetic with semiring-based operations to harmonize mathematics, software, and hardware. It introduces the idempotent correspondence principle and the dequantization paradigm, showing how core nonlinear problems such as the Hamilton–Jacobi and Bellman equations become linear over suitable semirings. The work extends to practical design by outlining universal algorithms, hardware prototypes (e.g., systolic processors), and a modular software architecture that supports multiple representations (real, interval, idempotent semirings). This framework aims to improve accuracy, safety, and speed of numerical computations through unified, parallelizable approaches across software and hardware.

Abstract

A unifying approach to software and hardware design generated by ideas of Idempotent Mathematics is discussed. The so-called idempotent correspondence principle for algorithms, programs and hardware units is described. A software project based on this approach is presented.