Applying the standard Boolean operations to closed regular sets may not produce a closed regular set, but this problem can be solved by regularizing the result of applying the standard Boolean operations.
32.
A "'compound path "'results from the combination of multiple paths ( inclusive and exclusive ) and the Boolean operations that ultimately determine what the combined path contains.
33.
(The circularity in this definition can be removed by replacing " finite Boolean algebra " by " finite power set " equipped with the Boolean operations standardly interpreted for power sets .)
34.
The Arithmetic and Logic Unit is responsible for performing boolean operations ( and, or, not, nand, nor, xor, xnor ) and also for performing integer addition and subtraction.
35.
The Boolean operations ( ",'" and ?used in ? are simulated in " p " ? by replacing the operators in ? as shown in the table below.
36.
Expressions involving variables and the Boolean operations represent statement forms, and two such expressions can be shown to be equal using the above axioms if and only if the corresponding statement forms are logically equivalent.
37.
In 2008, Win & Smolke designed a ribozyme regulator that could function in yeast cells that carried out Boolean operations similar to the earlier translational riboregulators, including AND, NOR, and OR gates.
38.
Since other Boolean operations, such as union or difference, may be expressed via intersection and complement operations, the sets of Nef polygons ( polyhedra ) are closed with respect to these operations as well.
39.
SAND CDBMS traces its roots to developments by Nucleus International Corporation research and eventual patent issued to, among others, Edward L . Glaser on Bit string compressor with boolean operation processing capability .
40.
Since then, this approach has been used to design efficient algorithms for a number of problems, such as construction of the Voronoi diagram ( Fortune's algorithm ) and the Delaunay triangulation or Boolean operations on polygons.
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