# Boolean logic

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## Synonyms for Boolean logic

### a system of symbolic logic devised by George Boole

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A boolean circuit over B with two inputs and one output, is a tuple C = (V, E, [alpha], [beta],[omega]), where (V, E) is a finite directed acyclic graph, [alpha]: E [right arrow] N is an injective function, [beta]: V [right arrow] B [union]{[x.
Thus, a boolean circuit C will compute a boolean function f:{0,1}2?
In the general case, when transforming a DAG into an equivalent tree, we may obtain a boolean circuit of exponential size in terms of its depth.
In this way, when we want to do the syntactic analysis of the FO formula, by each node corresponding to a logical connective or a quantifier, we will consider the boolean circuit structure that will generate such node, and consequently it will receive the appropriate weight and width.
We denote with D the difference of levels between both subtrees, according to the boolean circuit that represents v; this is D = P([v.
We present partial results of a research project in which we use boolean circuits as a parallel computation model for the expression of queries to relational databases.
The succinct representation of a binary word w is a Boolean circuit that on input of a number i (in binary), outputs whether i [is less than or equal to] |w| and in that case, the ith bit of w (|w| denotes the length of w).
We next describe disjunctive Datalog programs for deciding co-CERT3COL and for simulating a Boolean circuit.
I] be the Boolean circuit of an instance I of co-CERT3COL of size n.
Without loss of generality, we could bypass or-gates in the Boolean circuit simulation, by simulating or-gates with and-gates and not-gates.
For every Boolean circuit C, there exists an equivalent Boolean circuit C' that has O(|C|) size, so that C' has negation only immediately after input gates; moreover, such a C' can be easily constructed from C in logspace.
Am example is the CIRCUIT VALUE problem (compute the output of a Boolean circuit on a given input).
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