Some further comments on the DNA-protein coding problem

Abstract

A notion of quasi-ergodicity is defined in free monoids, generalizing a notion introduced in a previous paper (Rosen, 1959,Bull. Math. Biophysics,21, 71–95). It is shown that under certain conditions the algebraic properties of quasi-ergodicity are very similar to those derived for the more specialized concept inloc. cit. If it is assumed that the DNA-protein coding processes in nature are of a quasi-ergodic nature, then a condition is specified under which only a finite number of different DNA-protein codes are possible, and an upper bound for the total number of different quasi-ergodic codes is obtained.