# Boolean logic

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## Boolean logic

[boo´le-an]
an algebra that permits operations on sets of elements; it is used in online literature searches. The principal Boolean operators are AND (intersection), OR (union), and NOT (difference).
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Then any FO formula can be expressed as a subfamily of boolean circuits in the class Size-Depth(nO(1),log n).
Our goal is to get an equivalent subfamily of boolean circuits with logarithmic depth, i.
Translation of FO to Boolean Circuits When the atomic formula is interpreted for a given valuation, it is satisfied or no, that is, true or false.
Query Expressed as finite Subfamily of Boolean Circuits
r] -1, then we obtain a finite subfamily of boolean circuits C = {[C.
In this way, we construct the finite subfamily of boolean circuits that represents [phi]([x.
It is represented in the boolean circuits formalism by a circuit Ch, for some h, equivalent to ?
Generation of Suitable Equivalent Formulas for Parallelism The idea is, we have a FO formula then we want to find another equivalent, such that its expression tree has special characteristics that allow to obtain a finite subfamily of boolean circuits whose width and depth are suitable for the class NC1, this is Size- Depth([n.
Boolean circuits are a suitable theoretical model for the study of the computability and parallel complexity of queries to relational databases.
Given an r-ary query and a natural number n that represents the size of the domain of a given database, we showed how to build a finite subfamily of boolean circuits which preserves the property of uniformity, and which has a much better relation between size and depth, thus improving the time needed for the parallel evaluation of the query, as well as the appreciation of the parallelizability of the query.

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