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W1554694446 abstract "Given a Boolean function f, the quantity ess(f) denotes the largest set of assignments that falsify f, no two of which falsify a common implicate of f. Although ess(f) is clearly a lower bound on cnf_size(f) (the minimum number of clauses in a CNF formula for f), C˘epek et al. showed it is not, in general, a tight lower bound [6]. They gave examples of functions f for which there is a small gap between ess(f) and cnf_size(f). We demonstrate significantly larger gaps. We show that the gap can be exponential in n for arbitrary Boolean functions, and Θ(n) for Horn functions, where n is the number of variables of f. We also introduce a natural extension of the quantity ess(f), which we call essk(f), which is the largest set of assignments, no k of which falsify a common implicate of f." @default.
W1554694446 created "2016-06-24" @default.
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W1554694446 date "2013-01-01" @default.
W1554694446 modified "2023-09-30" @default.
W1554694446 title "On the gap between <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mstyle mathvariant=italic><mml:mi>ess</mml:mi></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si2.gif display=inline overflow=scroll><mml:mstyle mathvariant=italic><mml:mi>cnf_size</mml:mi></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:…" @default.
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W1554694446 doi "https://doi.org/10.1016/j.dam.2012.07.004" @default.
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