November 2018
Intermediate to advanced
1440 pages
48h 29m
English
Content preview from Computer Security Art and Science, 2nd Edition
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Appendix A
Lattices
A lattice is built on the notion of a group. First, we review some basic terms. Then we discuss lattices.
A.1 Basics
For a set S, a relation R is any subset of S × S. For convenience, if (a, b) ∊ R, we write aRb.
EXAMPLE: Let S = {1, 2, 3}. Then the relation less than or equal to is defined on S by the set R = {(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3)}. We write 1R2 and 2R3 for convenience, because (1, 2) ∊ R and (2, 3) ∊ R, but 3R2 does not hold, because (3, 2) ∉ R. Of course, the symbol used for R is simply ≤.
The following definitions describe properties of relations.
Definition A–1. A relation R defined over a set S is reflexive if aRa for all a ∊ S.
Definition A–2. A relation R defined over a set S is antisymmetric ...
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