Design by exmple: An application of Armstrong relations
Journal of Computer and System Sciences
On generating all maximal independent sets
Information Processing Letters
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
Data mining, hypergraph transversals, and machine learning (extended abstract)
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
New Results on Monotone Dualization and Generating Hypergraph Transversals
SIAM Journal on Computing
Hypergraph Transversal Computation and Related Problems in Logic and AI
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Attribute-incremental construction of the canonical implication basis
Annals of Mathematics and Artificial Intelligence
Some decision and counting problems of the Duquenne-Guigues basis of implications
Discrete Applied Mathematics
Pinpointing in the Description Logic $\mathcal {EL}^+$
KI '07 Proceedings of the 30th annual German conference on Advances in Artificial Intelligence
Some notes on pseudo-closed sets
ICFCA'07 Proceedings of the 5th international conference on Formal concept analysis
Counting pseudo-intents and #p-completeness
ICFCA'06 Proceedings of the 4th international conference on Formal Concept Analysis
Towards the Complexity of Recognizing Pseudo-intents
ICCS '09 Proceedings of the 17th International Conference on Conceptual Structures: Conceptual Structures: Leveraging Semantic Technologies
On the complexity of enumerating pseudo-intents
Discrete Applied Mathematics
Some complexity results about essential closed sets
ICFCA'11 Proceedings of the 9th international conference on Formal concept analysis
About the enumeration algorithms of closed sets
ICFCA'10 Proceedings of the 8th international conference on Formal Concept Analysis
Hardness of enumerating pseudo-intents in the lectic order
ICFCA'10 Proceedings of the 8th international conference on Formal Concept Analysis
Some notes on managing closure operators
ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
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We investigate the computational complexity of several decision, enumeration and counting problems related to pseudo-intents. We show that given a formal context and a subset of its set of pseudo-intents, checking whether this context has an additional pseudo-intent is in conp , and it is at least as hard as checking whether a given simple hypergraph is not saturated. We also show that recognizing the set of pseudo-intents is also in conp , and it is at least as hard as identifying the minimal transversals of a given hypergraph. Moreover, we show that if any of these two problems turns out to be conp -hard, then unless p = np , pseudo-intents cannot be enumerated in output polynomial time. We also investigate the complexity of finding subsets of a given Duquenne-Guigues Base from which a given implication follows. We show that checking the existence of such a subset within a specified cardinality bound is np -complete, and counting all such minimal subsets is #p -complete.