Additive cellular automata and algebraic series
Theoretical Computer Science
Hierarchy of fuzzy cellular automata
Fuzzy Sets and Systems
Cellular automata in fuzzy backgrounds
Physica D
Number-conserving cellular automaton rules
Fundamenta Informaticae - Special issue on cellular automata
Universality and decidability of number-conserving cellular automata
Theoretical Computer Science - Algorithms,automata, complexity and games
Number-conserving cellular automata I: decidability
Theoretical Computer Science
Number conserving cellular automata II: dynamics
Theoretical Computer Science
Fuzzy Cellular Automata for Modeling Pattern Classifier
IEICE - Transactions on Information and Systems
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
RBFFCA: A Hybrid Pattern Classifier Using Radial Basis Function and Fuzzy Cellular Automata
Fundamenta Informaticae - Special issue on DLT'04
Radial View of Continuous Cellular Automata
Fundamenta Informaticae - Membrane Computing
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Fuzzy cellular automata (FCA) are continuous cellular automata where the local rule is defined as the ''fuzzification'' of the local rule of a corresponding Boolean cellular automaton in disjunctive normal form. In this paper we are interested in the relationship between Boolean and fuzzy models and we analytically show, for the first time, the existence of a strong connection between them by focusing on two properties: density conservation and additivity. We begin by giving a probabilistic interpretation of our fuzzification which leads to two important results. First, it establishes an equivalence between convergent fuzzy CA and the mean field approximation on Boolean CA, an estimation of their asymptotic density. Second, we show that the density conservation property, extensively studied in the Boolean domain, is preserved in the fuzzy domain: a Boolean CA is density conserving if and only if the corresponding FCA is sum preserving. A similar result is established for another novel ''spatial'' density conservation property. Finally, we prove an interesting parallel between additivity of Boolean CA and oscillation of the corresponding fuzzy CA around its fixed point. In fact, we show that a Boolean CA has a certain form of additivity if and only if the behavior of the corresponding fuzzy CA around its fixed point coincides with the Boolean behavior. These connections between the Boolean and the fuzzy models are the first formal proofs of a relationship between them.