A Hierarchy of Monotone Deterministic Non-Forgetting Restarting Automata

The non-forgetting restarting automaton is an extension of the restarting automaton that is obtained by combining the restart operation with a change of the internal state just like the other operations. Thus, when executing a restart operation a non-forgetting restarting automaton is not forced to reset its internal state to its initial state. We analyze the expressive power of the deterministic variants of this model. As our main result we establish a hierarchy of language classes that are characterized by various types of monotone deterministic non-forgetting restarting automata. This hierarchy ranges from the deterministic context-free languages to the so-called left-to-right regular languages. In particular, we show that for monotone deterministic non-forgetting restarting automata, the RRWW-model is strictly more powerful than the RWW-model. This is the first time that for a particular type of restarting automaton the expressive power of the RRWW-variant is separated from the expressive power of the corresponding RWW-variant.