Enumerating minimal hypotheses and dualizing monotone boolean functions on lattices

Authors:
Mikhail A. Babin;Sergei O. Kuznetsov
Affiliations:
State University Higher School of Economics, Moscow, Russia;State University Higher School of Economics, Moscow, Russia
Venue:
ICFCA'11 Proceedings of the 9th international conference on Formal concept analysis
Year:
2011

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Abstract

Any monotone Boolean function on a lattice can be described by the set of its minimal 1 values. If a lattice is given as a concept lattice, this set can be represented by the set of minimal hypotheses of a classification context. Enumeration of minimal hypotheses in output polynomial time is shown to be impossible unless P = NP, which shows that dualization of monotone functions on lattices with quasipolynomial delay is hardly possible.