Two Lower Bounds for Circuits over the Basis (&, V, -)

A general approximation technique to get lower bounds for the complexity of combinational circuits over an arbitrary algebras of operations is presented. The technique generalizes recent methods for monotone circuits and yields some new results. This report contains an exp(Ω(log2n)) lower bound for the complexity of realization of non-monotone Boolean functions by circuits over the basis (&,V,-) computing sufficiently many prime implicants, and of three-valued functions by circuits over some incomplete three-valued extensions of (&,V,-).

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