## Combinatorial and Algorithmic Properties of One Matrix Structure at Monotone Boolean Functions

 Бакоев, Валентин (2019) Combinatorial and Algorithmic Properties of One Matrix Structure at Monotone Boolean Functions Cornell University Library, https://arxiv.org/abs/1902.06110 Резюме / Abstract  One matrix structure in the area of monotone Boolean functions is defined here. Some of its combinatorial, algebraic and algorithmic properties are derived. On the base of these properties, three algorithms are built. First of them generates all monotone Boolean functions of $n$ variables in lexicographic order. The second one determines the first (resp. the last) lexicographically minimal true (resp. maximal false) vector of an unknown monotone function $f$ of $n$ variables. The algorithm uses at most $n$ membership queries and its running time is $\Theta(n)$. It serves the third algorithm, which identifies an unknown monotone Boolean function $f$ of $n$ variables by using membership queries only. The experimental results show that for $1\leq n\leq 6$, the algorithm determines $f$ by using at most $m.n$ queries, where $m$ is the combined size of the sets of minimal true and maximal false vectors of $f$. Вид:   Статия Ключови думи:  monotone Boolean function, matrix structure properties, generating algorithm, minimal true vector, maximal false vector, identification algorithm Области: Природни науки, математика и информатика Математика Природни науки, математика и информатика Информатика и компютърни науки Subjects: Natural sciences, mathematics and informatics Mathematics Natural sciences, mathematics and informatics Informatics and Computer Science Статус:  Издадено Идентификационен номер:   24989 Автор:  Валентин Бакоев

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