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Since its introduction, Cartesian Genetic Programming has been mostly analyzed on an experimental level with boolean function problems. Consequently, there is still little theoretical understanding of Cartesian Genetic Programming. In this paper, we present a first time complexity analysis of Cartesian Genetic Programming. We introduce and analyze a simple mathematical problem and a simple logical boolean problem called SUM and AND. The results of our analysis show that simple CGP is able to solve SUM efficiently in time Θ(nlogn). However, our analysis of the AND problem shows that simple CGP is not able to solve AND efficiently.

On the Time Complexity of Simple Cartesian Genetic Programming