On Approximability of Boolean Formula Minimization

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 2, No 2, 129-135

Abstract: Abstract For a Boolean function $$f:\left\{ {0,1} \right\}^n \to \left\{ {0,1} \right\}$$ given by a Boolean formula (or a binary circuit) S we discuss the problem of building a Boolean formula (binary circuit) of minimal size, which computes the function g equivalent to $$f$$ , or ∈-equivalent to $$f$$ , i.e., $$Pr_{x \in \left\{ {0,1} \right\}^n } \left\{ {g\left( x \right) \ne f\left( x \right)} \right\} \leqslant \varepsilon $$ . In this paper we prove that if P ≠ NP then this problem can not be approximated with a “good” approximation ratio by a polynomial time algorithm.

Keywords: minimum formula size problem; minimum circuit size problem; approximation; Boolean circuits; Boolean formulas; inapproximability; combinatorial optimization (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOCO.0000031414.39556.3a

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