On generating all maximal independent sets
Information Processing Letters
Polynomial-time 1-Turing reductions from #PH to #P
Theoretical Computer Science
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Discovering all most specific sentences
ACM Transactions on Database Systems (TODS)
Normal forms for relational data bases.
Normal forms for relational data bases.
Theory of Relational Databases
Theory of Relational Databases
Subtractive reductions and complete problems for counting complexity classes
Theoretical Computer Science - Mathematical foundations of computer science 2000
Merge-Based computation of minimal generators
ICCS'05 Proceedings of the 13th international conference on Conceptual Structures: common Semantics for Sharing Knowledge
On computing the minimal generator family for concept lattices and icebergs
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
Counting pseudo-intents and #p-completeness
ICFCA'06 Proceedings of the 4th international conference on Formal Concept Analysis
Formal concept analysis in knowledge discovery: a survey
ICCS'10 Proceedings of the 18th international conference on Conceptual structures: from information to intelligence
Review: Formal Concept Analysis in knowledge processing: A survey on models and techniques
Expert Systems with Applications: An International Journal
Key roles of closed sets and minimal generators in concise representations of frequent patterns
Intelligent Data Analysis
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We investigate the computational complexity of some decision and counting problems related to generators of closed sets fundamental in Formal Concept Analysis. We recall results from the literature about the problem of checking the existence of a generator with a specified cardinality, and about the problem of determining the number of minimal generators. Moreover, we show that the problem of counting minimum cardinality generators is #ċcoNP-complete. We also present an incremental-polynomial time algorithm from relational database theory that can be used for computing all minimal generators of an implication-closed set.