Evolutionary Algorithms for Designing Reversible Cellular Automata

TL;DR

This paper explores using evolutionary algorithms to design reversible cellular automata with conserved landscapes, highlighting the challenges and potential applications in cryptography and reversible computing.

Contribution

It formulates the design of a specific class of reversible cellular automata as an optimization problem solved by genetic algorithms and programming, providing new insights into their complexity and properties.

Findings

Optimization of RCA is challenging for GA and GP.

Conserved landscape CA are relevant for cryptography.

Reversibility correlates with Hamming weight.

Abstract

Reversible Cellular Automata (RCA) are a particular kind of shift-invariant transformations characterized by a dynamics composed only of disjoint cycles. They have many applications in the simulation of physical systems, cryptography and reversible computing. In this work, we formulate the search of a specific class of RCA -- namely, those whose local update rules are defined by conserved landscapes -- as an optimization problem to be tackled with Genetic Algorithms (GA) and Genetic Programming (GP). In particular, our experimental investigation revolves around three different research questions, which we address through a single-objective, a multi-objective, and a lexicographic approach. The results obtained from our experiments corroborate the previous findings and shed new light on 1) the difficulty of the associated optimization problem for GA and GP, 2) the relevance of conserved landscape CA in the domain of cryptography and reversible computing, and 3) the relationship between the reversibility property and the Hamming weight.