Note: Automata on the plane vs particles and collisions

Authors:
N. Ollinger;G. Richard
Affiliations:
Laboratoire dinformatique fondamentale de Marseille (LIF), Aix-Marseille Université, CNRS, 39 rue Joliot-Curie, 13 013 Marseille, France;Laboratoire dinformatique fondamentale de Marseille (LIF), Aix-Marseille Université, CNRS, 39 rue Joliot-Curie, 13 013 Marseille, France
Venue:
Theoretical Computer Science
Year:
2009

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Universality of a reversible two-counter machine

Theoretical Computer Science - Special issue on universal machines and computations
Computation: finite and infinite machines

Computation: finite and infinite machines

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Abstract

In this note, colorings of the plane by finite sequential machines are compared to previously introduced notions of ultimately periodic tilings of the plane. Finite automata with no counter characterize exactly biperiodic tilings. Finite automata with one counter characterize exactly particles - periodic colorings that are ultimately periodic in every direction. Finite automata with two counters and aperiodic colorings characterize exactly collisions - ultimately periodic tilings of the plane.