One-Way Restarting Automata and Their Sensitivity

Here we establish and study some rigorous tools suitable for the lexicalized syntactic analysis (LSA) of natural and formal languages. Motivated by the linguistic method of analysis by reduction, we are interested in correctness preserving LSA. We introduce a suitable model of automata, the h-lexicalized one-way restarting automata (h-RRWW), and compare the properties of their input languages, which are the languages considered traditionally in automata theory, to the properties of the so-called basic and h-proper languages. These languages form the basic components for LSA. With respect to their input languages, h-RRWW-automata are not sensitive to the size of the read/write window and they allow computations that are far from being correctness preserving. On the other hand, for their basic and h-proper languages, h-RRWW-automata ensure that the resulting computations are completely correctness preserving, and they yield infinite ascending hierarchies of language classes within the regular, the context-free, and the context-sensitive languages that are based on the size of the read/write window.