Deterministic Automata for Unordered Trees

TL;DR

This paper introduces and analyzes notions of determinism for automata on unordered unranked trees, focusing on horizontal evaluation, and explores their computational properties and expressiveness.

Contribution

It proposes new notions of horizontal determinism for automata on unordered trees and studies their algorithmic and expressiveness implications.

Findings

Confluent horizontal evaluation enables polynomial-time emptiness and universality checks.

Imposing a global order on horizontal evaluation yields different automata classes with same expressiveness as CMso.

Efficient algorithms are achievable for certain deterministic automata classes.

Abstract

Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of determinism, which makes it difficult to distinguish subclasses of automata for which problems such as inclusion, equivalence, and minimization can be solved efficiently. In this paper, we propose and investigate different notions of "horizontal determinism", starting from automata for unranked trees in which the horizontal evaluation is performed by finite state automata. We show that a restriction to confluent horizontal evaluation leads to polynomial-time emptiness and universality, but still suffers from coNP-completeness of the emptiness of binary intersections. Finally, efficient algorithms can be obtained by imposing an order of horizontal evaluation globally for all automata in the class. Depending on the choice of the order, we obtain different classes of automata, each of which has the same expressiveness as CMso.