On the k-reversibility of finite automata

It is a famous result of Angluin (1982 [1]) that there exists a time poly- nomial and space linear algorithm to identify the canonical automata of kreversible languages by using characteristic sample sets. This result has several applications. In this paper we characterise the class of all automata for which her method is not applicable. In particular, the aim of this paper is to characterise the family of finite automata which are not k-reversible for any non-negative integer k