In this paper we introduce the class of linear non-deterministic automata with λ-transitions, and based on a new normal form for linear grammars, we prove that the class of languages accepted by such automata is exactly the class of linear languages. Also we show that, analogously to finite automata and pushdown automata, the ocorrences of λ-transitions in a non-deterministic linear automaton not means that not be possible define a non-deterministic linear automata without λ-transitions which accept the same language. Thus, λ-transitions not increases the acceptance power of this class of automata and therefore can be dispensed. Finally, we present an application of this automata in the context of bioinformatics.
Linear languages; linear grammars; normal form; non-deterministi linear automata; λ-transitions
