On the complexity of two-dimensional signed majority cellular automata

Eric Goles (1) , Pedro Montealegre (2) , Kévin Perrot (3) , Guillaume Theyssier (4)

1 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
2 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans
3 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
4 I2M - Institut de Mathématiques de Marseille

We study the complexity of signed majority cellular automata on the planar grid. We show that, depending on their symmetry and uniformity, they can simulate different types of logical circuitry under different modes. We use this to establish new bounds on their overall complexity, concretely: the uniform asymmetric and the non-uniform symmetric rules are Turing universal and have a P-complete prediction problem; the non-uniform asymmetric rule is in-trinsically universal; no symmetric rule can be intrinsically universal. We also show that the uniform asymmetric rules exhibit cycles of super-polynomial length, whereas symmetric ones are known to have bounded cycle length.

Mots clés: signed two-dimensional lattice; cellular automata dynamics; majority cellular automata; computational complexity; intrinsic universal; Turing universal

Domaines: Mathématique discrète [cs.DM]; Complexité [cs.CC]; Systèmes dynamiques [math.DS]

Eric Goles, Pedro Montealegre, Kévin Perrot, Guillaume Theyssier. On the complexity of two-dimensional signed majority cellular automata. Journal of Computer and System Sciences, 2018, 91, pp.1-32. ⟨hal-01472161v2⟩