China
Africa
Explore chapters and articles related to this topic
Boolean Algebra
Published in Richard L. Shell, Ernest L. Hall, Handbook of Industrial Automation, 2000
We now present another characterization of Boolean algebra. For a comprehensive treatment of lattice theory, see Birkhoff [5]. A lattice is a mathematical system (L, ∨, ∧) consisting of a nonempty set L = {a, b, c, …} and two binary operations ∨ (join) and ∧ (meet) defined on L such that:
Detecting all potential null dereferences based on points-to property sound analysis
Published in International Journal of Computers and Applications, 2020
Whether a pointer being dereferenced is a null dereference defect or not can be decided by its points-to property, and the points-to property can be described as an abstract lattice: ALPTR = (VPTR, Fjoin, Fmeet). The Hasse table of points-to property is shown in Figure 2, and VPTR depicts the value set of points-to property, which can describe security of a pointer being dereferenced effectively, and can be conveniently applied to null dereference detection. EMPTY expresses the initial value of property lattice, NULL expresses a pointer points to an illegal area, NOTNULL expressed a pointer points to a safe memory area, NON (NULL_OR_NOTNULL) expresses a pointer may be points to an illegal area. When a pointer is dereferenced, null dereference will inevitably occur if the points-to property of is NULL, and may occur if the points-to property is NON.
A New Metatheorem and Subdirect Product Theorem for L-Subgroups
Published in Fuzzy Information and Engineering, 2018
For a non empty set X, let denote the set of all crisp subsets of X, that is, the set of all functions from X to where ‘0’ is the minimal element and ‘1’ is the maximal element of L. Let be the ordinary power set of X. It is well known that is a complete lattice under the ordering of set inclusion where arbitrary join and meet are, respectively, the union and the intersection of an arbitrary family of subsets of X. Also, is a complete lattice under the usual ordering of L-set inclusion ⊆ and is a complete sublattice of . Recall that the function defined by , is a bijection from onto . Moreover, the following facts can be verified: The function chi commutes with arbitrary infs of and .The function chi commutes with arbitrary sups of and .
Logical Characterizations of Fuzzy Simulations
Published in Cybernetics and Systems, 2022
Linh Anh Nguyen, Ngoc-Thanh Nguyen
Given a residuated lattice let and denote the join and meet operators associated with the lattice. A residuated lattice is linear (respectively, complete) if the bounded lattice is linear (respectively, complete).