Minimum matrix representation of closure operations
✍ Scribed by J. Demetrovics; Z. Füredi; G.O.H. Katona
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 702 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
✦ Synopsis
matrix M and A a set of its columns. We say that A implies a iff M contains no two rows equal i n A but different i n a. It is easy IO see that if Y,~,(A) denotes . the columns implied by A, than :/,,,(A) is a closure operation.
We say that M represents this closure operation.
📜 SIMILAR VOLUMES
Let X be an n-element set and 2' be the family of subsets of X. If&C c 2' such that for any K. K\_ F .%'" K. f K\_ it-dim K. ct K. then Wr is ca!!pd a Sn~rtwr wstem Let \_M be 8~ ,+\_ x g \_\_l'\_\_L-~" '\_\_I , \_\_' \_\_\_\_=\_\_ \_\_ \_\_I i \_\_' \_ .
The system of all the closure operators on a set V forms a lattice. This lattice is isomorphic to the lattice of all the Moore families of subsets of V. This paper describes basic properties of these lattices, and gives a method to find all the members of these lattices.
Boolean operations akin to set intersection, union, and difference play an important role in CAD/CAM. Geometric entities of practical interest (e.g. polygons or polyhedra) are not algebraically closed under the conventional set operators, and therefore algorithms cannot implement conventional set op