Formally a boolean circuit can be defined as follows:

In the context of our work, a boolean circuit is defined as a directed acyclic graph (DAG), which is constructed by associating to each labelled node a variable, a constant or a boolean gate ([conjunction],[disconjunction],[logical not]), and by connecting the node gi to the node gj with an edge, whenever the output of the gate gi is an input to the gate gj .

Then, for each input length we must build a different boolean circuit.

Boolean circuit is one of such models, and has been extensively used in the last years.

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.

Our goal is to get an equivalent subfamily of boolean circuits with logarithmic depth, i.

Query Expressed as finite Subfamily of Boolean Circuits

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.