Minimum ε-equivalent Circuit Size Problem

Oleg A. Prokopyev () and Panos M. Pardalos ()
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Oleg A. Prokopyev: University of Florida
Panos M. Pardalos: University of Florida

Journal of Combinatorial Optimization, 2004, vol. 8, issue 4, No 6, 495-502

Abstract: Abstract For a Boolean function f given by its truth table (of length $$2^n$$ ) and a parameter s the problem considered is whether there is a Boolean function g $$\epsilon$$ -equivalent to f, i.e., $$Pr_{x\in {\{0,1\}}^n}\{g(x) \ne f(x)\} \le \epsilon$$ , and computed by a circuit of size at most s. In this paper we investigate the complexity of this problem and show that for specific values of $$\epsilon$$ it is unlikely to be in P/poly. Under the same assumptions we also consider the optimization variant of the problem and prove its inapproximability.

Keywords: minimum circuit size problem; approximation; Boolean circuits; inapproximability; natural properties; combinatorial optimization (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s10878-004-4839-5

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