Efficient exhaustive listings of reversible one dimensional cellular automata

Authors:
Tim Boykett
Affiliations:
Time's Up Research Department, Industriezeile 33b, A-4020 Linz, Austria and Department of Algebra, Johannes Kepler Universität, A-4040 Linz, Austria
Venue:
Theoretical Computer Science - Special issue: Theoretical aspects of cellular automata
Year:
2004

Citing 9
Cited 2

Generative communication in Linda

ACM Transactions on Programming Languages and Systems (TOPLAS)
Digraphs with walks of equal length between vertices

Graph theory with applications to algorithms and computer science
Ininvertible cellular automata: a review

Physica D
Reversibility of 2D cellular automata is undecidable

Physica D
The structure of reversible one-dimensional cellular automata

Physica D
Quasilinear cellular automata

Proceedings of the workshop on Lattice dynamics
Predicting nonlinear cellular automata quickly by decomposing them into linear ones

Physica D
An orderly algorithm and some applications in finite geometry

Discrete Mathematics
Isomorph-free exhaustive generation

Journal of Algorithms

Reversible computing and cellular automata—A survey

Theoretical Computer Science
Algebraic characterizations of unitary linear quantum cellular automata

MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science

Quantified Score

Hi-index	0.01

Visualization

Abstract

This paper looks at an algebraic formulation of one dimensional cellular automata. Using the formulation connections to combinatorial structures and graph theory become clear. Strong results about uniqueness and isomorphism allows us to outline effective algorithms for the generation of exhaustive lists of reversible one dimensional cellular automata, and to count the number of distinct examples that exist. These algorithms use the "orderly algorithm" methods to avoid the pitfalls of brute force searches.