Function induction, gene expression, and evolutionary representation construction

Different portions of the DNA, the primary information career of a living organism, are evaluated in different cells through the process of gene expression (DNA→mRNA→Protein). Such distributed evaluation of the fitness is possible only when its distributed representation using a set of basis functions is available in a living body. This paper argues that unless the evolution was provided with such a representation, we have every reason to believe that there must be an efficient mechanism to construct such a distributed representation. This paper considers functionally complete Walsh basis functions and shows that efficient polynomial-time computation of the Walsh representation (WR) is possible for problems with bounded non-linearity. It also offers a highly efficient algorithm O(2kr) to compute the WR for problems with non-negative Walsh coefficients, where r is the total number of non-zero terms in its WR.