The Queue Automaton Revisited

TL;DR

This paper demonstrates that non-deterministic queue automata are as expressive as Reactive Turing Machines, expanding the hierarchy of computational models with queues as a fundamental element.

Contribution

It establishes the equivalence in expressiveness between non-deterministic queue automata and Reactive Turing Machines, integrating queues into the hierarchy of executable process models.

Findings

Non-deterministic queue automata are as expressive as Reactive Turing Machines.

Queues are central elements in a hierarchy of computational models.

The hierarchy includes finite automata, pushdown automata, and parallel pushdown automata.

Abstract

We consider the computational model of the Queue Automaton. An old result is that the deterministic queue automaton is equally expressive as the Turing machine. We introduced the Reactive Turing Machine, enhancing the Turing machine with a notion of interaction. The Reactive Turing Machine defines all executable processes. In this paper, we prove that the non-deterministic queue automaton is equally expressive as the Reactive Turing Machine. Together with finite automata, pushdown automata and parallel pushdown automata, queue automata form a nice hierarchy of executable processes, with stacks, bags and queues as central elements.