Abstract
It is considered the general formulations and properties of cellular automata with cells which have the strong anticipatory property (introduced by D. Dubois). Multivalued behavior (hyperincursion) of solutions of such CA is described. It was posed new research problems of computation theory related to presumable multivaluedness of cellular automata with strong anticipation property. Extending of classical automata, Turing machine and algorithms had been proposed. Also some relation of such cellular automata and quantum mechanics are discussed.
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