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Finding all closed sets: A general approach. (English) Zbl 0754.06003

We present a unifying theoretical and algorithmic approach to the problems of determining all closed sets of a closure operator, doing this up to isomorphism, and determining the elements of certain ideals of a power set. This will be done by generalizing the concept of closure operators using the interplay of several orders of a power set.
Reviewer: K.Reuter

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
68R99 Discrete mathematics in relation to computer science
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References:

[1] B.Ganter (1987) Algorithmen zur formalen Begriffsanalyse, in B.Ganter, R.Wille, and K. E.Wolff, eds, Beitr?ge zur Begriffsanalyse, p. 241-254, B.I.-Wissenschaftsverlag, Mannheim, Wien, Z?rich.
[2] B. Ganter, Finding closed sets under symmetry, Preprint. · Zbl 0754.06003
[3] C.Read (1987) Every one a winner, or, how to avoid isomorphism search when cataloguing combinatorial configurations, Annals of Discr. Math. 2, 107-120. · Zbl 0392.05001
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