On the complexity of two-dimensional signed majority cellular automata

Eric Goles, Pedro Montealegre, Kévin Perrot, Guillaume Theyssier

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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 intrinsically 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.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalJournal of Computer and System Sciences
StatePublished - Feb 2018


  • Cellular automata dynamics
  • Computational complexity
  • Intrinsic universal
  • Majority cellular automata
  • Signed two-dimensional lattice
  • Turing universal


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