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


 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 $f$.
  Статия
 monotone Boolean function, matrix structure properties, generating algorithm, minimal true vector, maximal false vector, identification algorithm


Природни науки, математика и информатика Математика
Природни науки, математика и информатика Информатика и компютърни науки

Natural sciences, mathematics and informatics Mathematics
Natural sciences, mathematics and informatics Informatics and Computer Science

 Издадено
  24989
 Валентин Бакоев

Научният архив поддържа инициативата за отворен достъп OAI 2.0 с начален адрес: http://da.uni-vt.bg/oai2/