Some Remarks on the Π-directable Automata and Definite Automata: a Survey

The concept of π-directable automata is a concomitant specialization concept of the directable automata and generalization of the concept definite automata. The main purpose of this survey is to describe certain properties of πdirectable and definite automata. These are mainly algebraic and structural properties, as well as the properties of their transition semigroups. Various specializations and generalizations of directable automata are an interesting field of Automata theory. They have useful applications in industrial context and still offer open questions. There are applications in the fields of many-valued logics, biocomputing, set theory, etc.