Functional labels and syntactic entropy on DNA strings and proteins

AbstractThe DNA of a cell is an object which admits a simple mathematical description and a convenient representation in a computer (it is given by an easily manipulatable list, a finite sequence in four letters typically of length between one million and 10 billions). In contrast to this, there is no simple way of describing the cell neither statically and even less temporally (dynamically). We shall indicate here a possible formalism of combinatorial and numerical (entropic) structures on spaces of sequences which reflect, up to some degree, the organization and functions of DNA and proteins