1997/01/20 by Cristopher Moore · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics #adap-org #comp-gas #cond-mat.stat-mech #nlin.AO #nlin.CG
paper · pdf · doi:10.1023/b:joss.0000015172.31951.7b
10 pages with figures
arxiv created 1997/01/20 · openalex publication_date 1997/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to non-zero probability transitions in single spin-flip dynamics of the Ising model at zero temperature. We show that in three or more dimensions these systems can simulate Boolean circuits of AND and OR gates, and are therefore P-complete. That is, predicting their state t time-steps in the future is at least as hard as any other problem that takes polynomial time on a serial computer. Therefore, unless a widely believed conjecture in computer science is false, it is impossible even with parallel computation to predict majority-vote cellular automata, or zero-temperature single spin-flip Ising dynamics, qualitatively faster than by explicit simulation.