On linear languages recognized by deterministic biautomata

Abstract

We introduce the notion of a deterministic biautomaton, a device that reads inputs from both ends, and admits at most one computation on every input word. We show that deterministic biautomata recognize a class of languages which is properly included in the class of linear languages, and which is incomparable to the class of languages recognized by deterministic one-turn pushdown automata. We propose three restrictions of the basic model of deterministic biautomata to characterize the classes of languages generated by DL, linear LL(1), and NH-DL grammars. This results in a chain of four subclasses of linear languages in which all inclusions are strict. For these subclasses and basic operations, we show whether or not a particular class is closed under a considered operation. We prove that it is undecidable whether a linear language belongs to any of these four classes and answer some other decidability questions.