Hyper-Minimization for Deterministic Register Automata

2026-05-05

AI Summary

This study addresses the hyper-minimization problem for well-typed deterministic register automata (DRA), which seeks to simultaneously minimize both the number of states and the number of registers. Building upon analogues of classical finite automaton concepts adapted to the DRA setting, the work establishes a theoretical foundation and proposes a specialized algorithm grounded in register-type analysis, equivalence relations, and refinement techniques. This is the first approach to achieve joint minimization of states and registers for well-typed DRAs, thereby proving the decidability of the hyper-minimization problem. The resulting automaton is rigorously shown to attain global optimality in both state count and register count among all well-typed DRAs recognizing the same language.

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.

Problem

• hyper-minimization
• deterministic register automata
• well-typed
• minimality
• register automata

Innovation

• hyper-minimization
• deterministic register automata
• well-typed
• state minimization
• register minimization