Smooth Maps of the Interval and the Real Line Capable of Universal Computation

Christopher Moore

Working Papers from Santa Fe Institute

Abstract: We construct two classes of maps: once-differentiable maps of the unit interval which can simulate a wide variety of operations on sequences, including cellular automata, generalized shifts, and Turing machines; and analytic maps of $R$ which simulate Turing machines. This brings down the dimensionality in which a smooth dynamical system can be computationally universal from 2 [1] to 1.

Date: 1993-01
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Persistent link: https://EconPapers.repec.org/RePEc:wop:safiwp:93-01-001

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