The Queue Automaton Revisited

TL;DR

The paper investigates the expressive power of nondeterministic queue automata and their relation to Reactive Turing Machines ($\mathrm{RTM}$), situating queue automata within a hierarchy of executable processes. It formalizes queue automata, languages, and branching bisimilarity, and proves robustness across one- and two-queue variants, while establishing equivalence with RTMs. It shows that executable processes can be captured as regular processes interacting with a queue using the process algebra $BCP_{\tau}$ and related translations, including a universal queue automaton construction. Overall, the work unifies automata theory and concurrency theory, highlights a clear memory-based hierarchy centered on queues, and refines the notion of executability across memory models.

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.

Figures (8)

• Figure 1: Queue automaton for the language $\{ ww \mid w \in \{a,b\}^{*} \}$.
• Figure 2: Queue automaton for the language $\{ a^nb^nc^n \mid n>0\}$.
• Figure 3: Queue automata of the queue.
• Figure 4: Queue automaton for the function $f(w) = ww$ on $\{a,b\}^{*}$.
• Figure 5: Queue automaton comparing quantities.

Theorems & Definitions (34)

• Definition 1
• Definition 2
• Definition 3
• Theorem 1
• proof
• Definition 4
• Definition 5: Queue automaton
• Definition 6
• Definition 7
• Example 1