2022/10/03 by Xuan Kien Phung, Phung, Xuan Kien
Computer Science · #05C25 #20F69 #37B10 #37B15 #37B51 #68Q80 #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #Coding theory and cryptography #Computation and Language (cs.CL) #Distributed #Dynamical Systems (math.DS) #F.1.1 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Parallel #Quantum-Dot Cellular Automata #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2210.00676
openalex publication_date 2022/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For non-uniform cellular automata (NUCA) with finite memory over an arbitrary universe with multiple local transition rules, we show that pointwise nilpotency, pointwise periodicity, and pointwise eventual periodicity properties are respectively equivalent to nilpotency, periodicity, and eventual periodicity. Moreover, we prove that every linear NUCA which satisfies pointwise a polynomial equation (which may depend on the configuration) must be an eventually periodic linear NUCA. Generalizing results for higher dimensional group and linear CA, we also establish the decidability results of the above dynamical properties as well as the injectivity for arbitrary NUCA with finite memory which are local perturbations of higher dimensional linear and group CA. Some generalizations to the case of sparse global perturbations of higher dimensional linear and group CA are also obtained.