Titlebook: Solvable Cellular Automata; Methods and Applicat Henryk Fukś Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive lic

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Probabilistic Solutions,istic initial value problem and examples of its solutions. Probabilistic solutions for rule 172 and for additive rules. Examples of higher order probabilistic solutions. Rules 184 and 14. Surjectivity and the balance theorem. Probabilistic solutions for surjective rules.

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Applications,ased on rule 184. Critical slowing down. First and second order phase transitions in CA. Solution of the density classification problem with two CA rules. Finite size effects in rule 172. Using deterministic solutions to verify equicontinuity.

顶点

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frenzy

Multiplicative and Additive Rules,Multiplicative rules. Solutions of the IVP for rules 23 and 140. Additive or linear rules and their solutions. Solutions of the IVP for rules 132 and 77.

Digest

More Complex Rules,Construction of solutions of the IVP by exploiting patterns in preimage sequences. Rules 172, 168 and 164. Pattern decomposition method. Solutions of rules 156 and 78.

高谈阔论

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Construction of the Probability Measures,Cylinder sets and their semi-algebra. Finitely additive maps. Hahn-Kolmogorov extension theorem. Shift-invariant measures and consistency conditions. Block probabilities and their representations by probabilities of short and long blocks.

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Probabilistic Cellular Automata,Probabilistic cellular automata viewed as a Markov process. Maps in the space of measures. Orbits of probability measures and the probabilistic initial value problem. Single transition alpha-asynchronous rules. Application of the cluster expansion formula to solve the probabilistic IVP. Special cases of rules 206, 222, 236, 238 and 254.

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Approximate Methods,Bayesian extension and Markov measures. Weak convergence of Markov measures. Local structure approximation of orbits of measures. Local structure maps and their examples for deterministic and probabilistic cellular automata. Quality of the local structure approximation. Minimal entropy approximation.