Scoped MSO, Register Automata, and Expressions: Equivalence over Data Words
Abstract
This paper establishes logical and expression-based characterizations for the class of languages recognized by nondeterministic register automata with guessing (NRA) over infinite alphabets. We introduce Scoped MSO, a logic featuring a novel segment modality and syntactic restrictions on data comparisons. We prove this logic is expressively equivalent to NRA over data domains where ``strong guessing'' can be eliminated. Furthermore, we define Data-Regular Expressions, a minimalist regular-expression calculus built from quantifier-free regions and equipped with -contracting concatenation, and demonstrate its equivalence to NRA over arbitrary relational structures. Together, these formalisms provide a robust descriptive theory for register automata, bridging the gap between automata, logic, and expressions.
Cite
@article{arxiv.2602.13120,
title = {Scoped MSO, Register Automata, and Expressions: Equivalence over Data Words},
author = {Radosław Piórkowski},
journal= {arXiv preprint arXiv:2602.13120},
year = {2026}
}