Symbolic Regression of Boolean Functions by Genetic Programming

Abstract

An evolutionary metaphor of genetic programming for a symbolic regression of Boolean functions, which represent logic circuits, is studied. These functions are coded by acyclic oriented graphs with vertices corresponding to elementary Boolean operations, e. g. negation, conjunction, disjunction (both inclusive and exclusive), and their negations. The used acyclic oriented graphs are represented by the so-called column tables. Basic "genetic" operations of mutation and crossover are performed over these column tables. Preliminary results indicate that the proposed version of genetic programming with column tables is an effective evolutionary tool for a construction of optimized Boolean functions that are specified by tables of functional values for all possible combinations of arguments. © Springer-Verlag Berlin Heidelberg 2013.