Rice's theorem for the limit sets of cellular automata
Theoretical Computer Science
Models of massive parallelism: analysis of cellular automata and neural networks
Models of massive parallelism: analysis of cellular automata and neural networks
Finite fields
Foundations of computing
Signals in one-dimensional cellular automata
Theoretical Computer Science - Special issue: cellular automata
Generation of Primes by a One-Dimensional Real-Time Iterative Array
Journal of the ACM (JACM)
On computing the entropy of cellular automata
Theoretical Computer Science
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
Real-time language recognition by one-dimensional cellular automata
Journal of Computer and System Sciences
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Information dynamics of cellular automata(CA) is studied using polynomials over finite fields. The information about the uncertainty of cell states is expressed by an indeterminate X called information variable and its dynamics is investigated by extending CA to CA[X] whose cell states are polynomials in X. For the global configuration of extended CA[X], new notions of completeness and degeneracy are defined and their dynamical properties are investigated. A theorem is proved that completeness equals non-degeneracy. With respect to the reversibility, we prove that a CA is reversible, if and only if its extension CA[X] preserves the set of complete configurations. Information dynamics of finite CAs and linear CAs are treated in the separate sections. Decision problems are also referred.