An Algorithmic Pipeline for Solving Equations over Discrete Dynamical Systems Modelling Hypothesis on Real Phenomena

TL;DR

This paper introduces an algorithmic pipeline to analyze finite discrete dynamical systems, enabling the validation of hypotheses about their intrinsic structure and asymptotic behavior in modeling real phenomena.

Contribution

It presents a novel pipeline for solving equations over DDS to study their intrinsic structure, with proven soundness and completeness, advancing analysis of complex dynamical models.

Findings

Pipeline is sound and complete for analyzing DDS

Enables validation of hypotheses on system behavior

Provides algebraic tools for studying intrinsic structure

Abstract

This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under observation, the feature of resulting from the "cooperation" of the dynamics of two or more smaller DDS. The intrinsic structure is described by an equation over DDS which represents a hypothesis over the phenomenon under observation. The pipeline allows solving such an equation, i.e., validating the hypothesis over the phenomenon, as far the asymptotic behavior and the number of states of the DDS under observation are concerned. The results are about the soundness and completeness of the pipeline and they are obtained by exploiting the algebraic setting for DDS introduced in [10].