## A Striking Property of Genetic Code-like Transformations

**Hillol Kargupta***Electronic mail address: hillol@cs.umbc.edu**Department of Computer Science and Electrical Engineering,**University of Maryland Baltimore County,**Baltimore, MD 21250, USA*

#### Abstract

The gene expression process in nature plays a key role in evaluating the fitness of DNA through the production of different proteins in different cells. The production of proteins from DNA goes through different stages. Among others, the transcription stage produces the mRNA from the DNA and translation produces the amino acid sequence in proteins from the mRNA. The translation process is accomplished by mapping the mRNA sequence using a transformation called the *genetic code*. This code considers every consequent triplet (codon) of nucleic acids in the mRNA sequence and maps it to a corresponding amino acid. This paper shows that genetic code-like transformations (GCTs) introduce very interesting properties to the representation of a genetic fitness function. It presents a Fourier (The analysis is identical to that using Walsh basis [4, 45]; however, the term Fourier is chosen because of its historical [18, 32] use in function approximation literature.) analysis of GCTs. It points out that such transformations can convert some function representations of exponential description in Fourier basis to a description that is highly suitable for polynomial-complexity approximation. More precisely, such transformations can construct a Fourier representation with only a polynomial number of terms that are exponentially more significant than the rest. Polynomial-complexity approximation of functions from data is a fundamental problem in inductive learning, data mining, search, and optimization. Therefore the work has important implications in these areas. It is unlikely that such representations can be constructed for all functions. However, since such transformations appear to work well in nature, the class of such functions may not be trivial and should be explored further.