Computation in Genetic Code-Like Transformations

The gene expression process in nature evaluates the tness of a DNA through the production of di erent proteins in di erent cells. The DNA sequence rst produces the mRNA sequence and the mRNA produces protein by using a transformation called the genetic code[1]. It has been shown [2]that genetic code-like transformations introduce very interesting properties to the representation of a genetic tness function. Such transformations can convert functions with exponentially large description in Fourier basis to one that is highly suitable for polynomial-size approximation. Such transformations can construct a Fourier representation with only a polynomial number of terms that are exponentially more signi cant than the rest when tter chromosomes are given more copies through a redundant, equivalent representation. This is a very desirable property for eÆcient induction of function representation from data which is a fundamental problem in learning, data mining, and optimization.