  In this paper we consider the class of lambda-nondeterministic linear
automata as a model of the class of linear languages. As usual in other
automata models, lambda-moves do not increase the acceptance power. The main
contribution of this paper is to introduce the deterministic linear automata
and even linear automata, i.e. the natural restriction of nondeterministic
linear automata for the deterministic and even linear language classes,
respectively. In particular, there are different, but not equivalents,
proposals for the class of "deterministic" linear languages. We proved here
that the class of languages accepted by the deterministic linear automata are
not contained in any of the these classes and in fact they properly contain
these classes. Another, contribution is the generation of an infinite hierarchy
of formal languages, going from the class of languages accepted by
deterministic linear automata and achieved, in the limit, the class of linear
languages.
