Algorithm as Defining Dynamic Systems

TL;DR

This paper introduces a novel perspective on algorithms as dynamic systems defined by laws, advocating for a two-step development process involving natural language laws and formal translation.

Contribution

It proposes viewing algorithms as dynamic systems with defining laws and outlines a two-step design approach using natural language and formal logic.

Findings

New framework for algorithm design as dynamic systems

Two-step process for translating natural language laws into formal logic

Potential for more flexible and expressive algorithm development

Abstract

This paper proposes a new view to algorithms, Algorithms as defining dynamic systems. This view extends the traditional, deterministic view that an algorithm is a step by step procedure with nondeterminism. As a dynamic system can be designed by a set of its defining laws, it is also desirable to design an algorithm by a (possibly nondeterministic) set of defining laws. This observation requires some changes to algorithm development. We propose a two step approach, the first step is to design an algorithm via a set of defining laws of dynamic system. The second step is to translate these laws (written in a natural language) into a formal language such as linear logic.