Journal of Combinatorial Optimization

, Volume 8, Issue 4, pp 495–502 | Cite as

Minimum ε-equivalent Circuit Size Problem

  • Oleg A. Prokopyev
  • Panos M. Pardalos


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.

minimum circuit size problem approximation Boolean circuits inapproximability natural properties combinatorial optimization 


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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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