Some decision and counting problems of the Duquenne-Guigues basis of implications

Authors:
Sergei O. Kuznetsov;Sergei Obiedkov
Affiliations:
Department of Applied Mathematics, State University Higher School of Economics, Moscow, Russia;Department of Computer Science, University of Pretoria, Pretoria, South Africa
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

Implications of a formal context obey Armstrong rules, which allows one to define a minimal (in the number of implications) implication basis, called Duquenne-Guigues basis or stem base in the literature. In this paper we show how implications are reduced to functional dependencies and prove that the problem of determining the size of the stem base is a #P-complete problem.