Complexity of identification and dualization of positive Boolean functions
Information and Computation
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
On Maximal Frequent and Minimal Infrequent Sets in Binary Matrices
Annals of Mathematics and Artificial Intelligence
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Associating categories with measured or observed attributes is a central challenge for discrete mathematics in life sciences. We propose a new concept to formalize this question: Given a binary matrix of objects and attributes, determine all attribute sets characterizing object sets of cardinality t"1 that do not characterize any object set of size t"2t"1. We determine how many such attribute sets exist, give an output-sensitive quasi-polynomial time algorithm to determine them, and show that k-sum matrix decompositions known from matroid theory are compatible with the characterization.