Input-Driven Queue Automata with Internal Transductions

Abstract

For input-driven queue automata (\(\text {IDQA}\)) the input alphabet is divided into three distinct classes and the actions on the queue (enter, remove, nothing) are solely governed by the input symbols. Here, this model is extended in such a way that the input of an \(\text {IDQA}\) is preprocessed by an internal deterministic sequential transducer. These automata are called tinput-driven queue automata (\(\text {TDQA}\)). It turns out that even \(\text {TDQA}\)s with weak, that is, deterministic injective and length-preserving, internal transducers are more powerful than \(\text {IDQA}\)s. We study closure properties of the family of languages accepted by \(\text {TDQA}\)s. For example, for compatible signatures the closure under the Boolean operations union, intersection, and complementation is shown. For incompatible signatures and the operations reversal, concatenation, iteration, and length-preserving homomorphism non-closure results are obtained. Depending on the working mode of the transducer and the \(\text {IDQA}\), there are three nondeterministic working modes for tinput-driven queue automata. It is shown that for devices with nondeterministic transducers the nondeterministic \(\text {IDQA}\) can be determinized. The other classes form a strict hierarchy. Finally, several decidability problems are addressed.