Algebraic design of physical computing system

Recently, computational techniques that employ physical systems (physical computing systems) have been developed. To utilize physical computing systems, their design strategy is important. Although there are practical learning-based methods and theoretical approaches, no general method exists that provides specific design guidelines for given systems with rigorous theoretical support. In this paper, we propose a novel algebraic design framework for a physical computing system, which is capable of extracting specific design guidelines. Our approach describes input–output relationships algebraically and relates them to given target tasks. Two theorems are presented in this paper. The first theorem offers a basic strategy for algebraic design. The second theorem explores the “replaceability” of such systems. Their possible implementations are investigated through experiments. In particular, the design of inputs of a system so that it generates multiple target time-series and the replacement of stationary or non-stationary target systems by a given system that is designed algebraically are included. The proposed framework is shown to have the potential of designing given physical computing systems with theoretical support.