Chebyshev polynomials over finite fields and reversibility of σ-automata on square grids

Authors:
Markus Hunziker;António Machiavelo;Jihun Park
Affiliations:
Department of Mathematics, University of Georgia, Athens, GA;Centro de Matemática da Universidade do Porto, Porto 4169-007, Portugal;Department of Mathematics, POSTECH, Pohang, Kyungbuk 790-784, Republic of Korea
Venue:
Theoretical Computer Science
Year:
2004

Citing 7
Cited 3

Merlin's magic square

American Mathematical Monthly
The &sgr;-game and cellular automata

American Mathematical Monthly
σ-game, σ+-game and two-dimensional additive cellular automata

Theoretical Computer Science
Multidimensional &sgr;-automata, &pgr;-polynomials and generalised S-matrices

Theoretical Computer Science
&sgr;-Automata and Chebyshev-polynomials

Theoretical Computer Science
Universal configurations in light-flipping games

SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information

The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information

Note: Minimum light number of lit-only σ-game on a tree

Theoretical Computer Science
Does the lit-only restriction make any difference for the σ-game and σ+-game?

European Journal of Combinatorics
A singular quartic curve over a finite field and the Trisentis game

Finite Fields and Their Applications

Quantified Score

Hi-index	5.23

Visualization

Abstract

Using number theory on function fields and algebraic number fields, we prove results about Chebyshev polynomials over finite prime fields to investigate reversibility of two-dimensional additive cellular automata on finite square grids. For example, we show that there are infinitely many primitive irreversible additive cellular automata on square grids when the base field has order two or three.