Real Computation with Cellular Automata

Two definitions about computability of real-valued functions by cellular automata are proposed, each requiring exact computation (unlike Turing-based computability). Recursive functions, some polynomials, and even logistic and chaotic maps are shown to be exactly computable even under discrete space, time and states of the computer model, on representations more general than standard signed expansions. A number of consequences of these definitions are presented that point to computational primitives different from classical continuous objects based on addition and multiplication. Several open questions pertaining characterization of real-valued functions computable by cellular automata are briefly discussed, notably the encoding/representation problem and the halting criterion.

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