Given a continuous function $f(x)$, suppose that the sign of $f$ only has finitely many discontinuous points in the interval $[0,1]$. We show how to use a sequence of one dimensional deterministic binary cellular automata to determine the sign of $f(rho)$ where $rho$ is the (number) density of 1s in an arbitrarily given bit string of finite length provided that $f$ satisfies certain technical conditions.
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