Initial value problem of evolution equations defined by lattice operators

TL;DR

This paper introduces lattice equations as dynamical systems on lattice algebras, provides exact solutions for initial value problems, analyzes their complexity, and explores their connection to binary cellular automata.

Contribution

It presents the first exact solutions for a class of lattice equations and investigates their relation to cellular automata, advancing understanding of lattice-based dynamical systems.

Findings

Exact solutions for initial value problems of lattice equations

Complexity analysis of the solutions

Relationship established between lattice equations and cellular automata

Abstract

We propose dynamical systems defined on algebra of lattices, which we call `lattice equations'. We give exact general solutions of initial value problems for a class of lattice equations, and evaluate the complexity of the solutions. Moreover we discuss the relationship between those equations and binary cellular automata.