On some properties of systems. a survey

From some time past our interest was focused to find new possibilities for characterizing the process of generation of the words by generative systems. In some of our papers we have introduced some numerical functions able to characterize classes of derivations according to a given generative system (as the phrase-structure grammars known in formal languages) up to an equivalence. They are referred to as "derivational functions". In this paper we consider equivalence classes of derivations and we establish some new properties of symmetry and invariance. Then, some aspects regarding to the Markov property in a vision of Kiyosi Itô are discussed. Finally we refer to some results concerning the reliable systems due especially to A. D. Solovyev and B. V. Gnedenko.