One-dimensional cellular automata with random rules: longest temporal period of a periodic solution

DOI10.1214/22-EJP744MaRDI QIDQ2119677

Xiaochen Liu, Janko Gravner

Publication date: 30 March 2022

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.06914

zbMATH Keywords

periodic solutionBrownian bridgecellular automatonrandom rule

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Dynamical aspects of cellular automata (37B15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Periodic points for onto cellular automata
• Iterations of linear maps over finite fields
• Algebraic properties of cellular automata
• Computation theory of cellular automata
• Random sequence generation by cellular automata
• Global properties of cellular automata
• Cylindrical cellular automata
• Periodic solutions of nonlinear dynamical systems. Numerical computation, stability, bifurcation and transition to chaos
• Maximum length cellular automaton sequences and its application
• Logarithmic combinatorial structures: A probabilistic approach
• Brownian bridge asymptotics for random \(p\)-mappings
• On the construction of state diagrams for cellular automata with additive rules
• On the weak convergence of interpolated Markov chains to a diffusion
• Robust periodic solutions and evolution from seeds in one-dimensional edge cellular automata
• Transient and cyclic behavior of cellular automata with null boundary conditions
• ON THE DYNAMICAL BEHAVIOR OF CELLULAR AUTOMATA
• Closed-form Expressions for the Moments of the Binomial Probability Distribution
• Limit Theorems for Combinatorial Structures via Discrete Process Approximations
• Brownian bridge asymptotics for random mappings
• Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2)
• Compound random mappings
• Generating Cryptographically Suitable Non-linear Maximum Length Cellular Automata
• Maximal temporal period of a periodic solution generated by a one-dimensional cellular automaton
• Jointly Periodic Points in Cellular Automata: Computer Explorations and Conjectures
• STACS 2005
• Linear cellular automata and recurring sequences in finite fields

This page was built for publication: One-dimensional cellular automata with random rules: longest temporal period of a periodic solution