@TechReport{Langdon98, author = "William B Langdon and Riccardo Poli", title = {Boolean Functions Fitness Spaces}, institution = {University of Birmingham, School of Computer Science}, number = {CSRP-98-16}, month = {June}, year = {1998}, email = {W.B.Langdon@cs.bham.ac.uk, R.Poli@cs.bham.ac.uk}, file = {/1998/CSRP-98-16.ps.gz}, url = {ftp://ftp.cs.bham.ac.uk/pub/tech-reports/1998/CSRP-98-16.ps.gz}, abstract = {We investigate the distribution of performance of the Boolean functions of 3 Boolean inputs (particularly that of the parity functions), the always-on-6 and even-6 parity functions. We us enumeration, uniform Monte-Carlo random sampling and sampling random full trees. As expected XOR dramatically changes the fitness distributions. In all cases once some minimum size threshold has been exceeded, the distribution of performance is approximately independent of program length. However the distribution of the performance of full trees is different from that of asymmetric trees and varies with tree depth. We consider but reject testing the No Free Lunch (NFL) theorems on these functions. }, }