Hyper-Minimization for Deterministic Register Automata

TL;DR

This paper introduces a hyper-minimization algorithm for well-typed deterministic register automata, proving its correctness and establishing the decidability of this minimization process.

Contribution

It develops the first hyper-minimization algorithm for well-typed DRAs and proves its correctness and decidability.

Findings

Automata are minimal in states and registers among well-typed DRAs.

The algorithm's correctness is formally proven.

Decidability of hyper-minimization for well-typed DRAs is established.

Abstract

We investigate hyper-minimization for deterministic register automata (DRAs). We begin by introducing DRA counterparts of classical notions from deterministic finite automata. Building on these foundations, we present an algorithm for hyper-minimizing well-typed DRAs, where each state is associated with a unique register type. The resulting automata are minimal with respect to both the number of states and registers among all well-typed DRAs. We prove the correctness of the proposed algorithm, thereby establishing the decidability of hyper-minimization for well-typed DRAs.