The Containment Problem for Unambiguous Register Automata

TL;DR

This paper studies the containment problem for unambiguous register automata, proving its decidability and analyzing the computational complexity under various restrictions.

Contribution

It establishes the decidability of the containment problem for unambiguous register automata and provides complexity bounds for different cases.

Findings

Containment problem is decidable for unambiguous register automata.

Complexity bounds are provided for general and fixed-register cases.

The results advance understanding of automata containment in data automata theory.

Abstract

We investigate the complexity of the containment problem "Does $L(A)\subseteq L(B)$ hold?", where $B$ is an unambiguous register automaton and $A$ is an arbitrary register automaton. We prove that the problem is decidable and give upper bounds on the computational complexity in the general case, and when $B$ is restricted to have a fixed number of registers.