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Minimum Implicational Basis for -Semidistributive Lattices

Abstract : For a ∧-semidistributive lattice L, we study some particular implicational systems and show that the cardinality of a minimum implicational basis is polynomial in the size of join-irreducible elements of the lattice L. We also provide a polynomial time algorithm to compute a minimum implicational basis for L.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00101743
Contributor : Martine Peridier <>
Submitted on : Thursday, September 28, 2006 - 9:54:58 AM
Last modification on : Wednesday, April 21, 2021 - 8:52:04 AM
Long-term archiving on: : Monday, April 5, 2010 - 11:56:00 PM

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  • HAL Id : lirmm-00101743, version 1

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Philippe Janssen, Lhouari Nourine. Minimum Implicational Basis for -Semidistributive Lattices. Information Processing Letters, Elsevier, 2006, 99 (5), pp.199-202. ⟨lirmm-00101743⟩

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