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• W2023134879 abstract "We consider the problem of identifying an unknown Boolean function f by asking an oracle the functional values $f(a)$ for a selected set of test vectors $a in {0,1}^{n}$. Furthermore, we assume that f is a positive (or monotone) function of n variables. It is not yet known whether or not the whole task of generating test vectors and checking if the identification is completed can be carried out in polynomial time in n and m, where $m=|min T(f)| + |max F(f)|$ and $min T(f)$ (respectively, $max F(f))$ denotes the set of minimal true (respectively, maximal false) vectors of f. To partially answer this question, we propose here two polynomial-time algorithms that, given an unknown positive function f of n variables, decide whether or not f is 2-monotonic and, if f is 2-monotonic, output both sets $min T(f)$ and $max F(f)$. The first algorithm uses $O(nm^{2} + n^{2}m)$ time and $O(nm)$ queries, while the second one uses $O(n^{3}m)$ time and $O(n^{3}m)$ queries." @default.
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• W2023134879 date "1997-02-01" @default.
• W2023134879 modified "2023-09-26" @default.
• W2023134879 title "Polynomial-Time Recognition of 2-Monotonic Positive Boolean Functions Given by an Oracle" @default.
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• W2023134879 doi "https://doi.org/10.1137/s0097539793269089" @default.
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