2 research outputs found
A Note on the Inversion Complexity of Boolean Functions in Boolean Formulas
In this note, we consider the minimum number of NOT operators in a Boolean
formula representing a Boolean function. In circuit complexity theory, the
minimum number of NOT gates in a Boolean circuit computing a Boolean function
is called the inversion complexity of . In 1958, Markov determined the
inversion complexity of every Boolean function and particularly proved that
NOT gates are sufficient to compute any Boolean
function on variables. As far as we know, no result is known for inversion
complexity in Boolean formulas, i.e., the minimum number of NOT operators in a
Boolean formula representing a Boolean function. The aim of this note is
showing that we can determine the inversion complexity of every Boolean
function in Boolean formulas by arguments based on the study of circuit
complexity.Comment: 5 pages, 1 figure
A Note on the Inversion Complexity of Boolean Functions in Boolean Formulas
In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f. In 1958, Markov determined the inversion complexity of every Boolean function and particularly proved that βlog 2(n + 1) β NOT gates are sufficient to compute any Boolean function on n variables. As far as we know, no result is known for inversion complexity in Boolean formulas, i.e., the minimum number of NOT operators in a Boolean formula representing a Boolean function. The aim of this note is showing that we can determine the inversion complexity of every Boolean function in Boolean formulas by arguments based on the study of circuit complexity.