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In this paper, we define and study the k-approximating circuits. A circuit accepting a given set of inputs A is k-approximated by accepting inputs that differ from one of A by at most k bits. We show that the existence of polynomial-size k-approximating circuits depends on the relation between k and the number of inputs.
Reliability and testing, complexity measures and classes, models of computation.

P. Liberatore, M. Schaerf, F. M. Donini and M. Cadoli, "k-Approximating Circuits," in IEEE Transactions on Computers, vol. 55, no. , pp. 913-917, 2006.
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