Deterministic Automata for Unordered Trees

Adrien Boiret
(University of Lille 1. Links (Inria Lille & LIFL, UMR CNRS 8022), France )
Vincent Hugot
(Inria. Links (Inria Lille & LIFL, UMR CNRS 8022), France )
Joachim Niehren
(Inria. Links (Inria Lille & LIFL, UMR CNRS 8022), France )
Ralf Treinen
(University Paris Diderot. PPS (UMR CNRS 7126), France )

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.

In Adriano Peron and Carla Piazza: Proceedings Fifth International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2014), Verona, Italy, 10th - 12th September 2014, Electronic Proceedings in Theoretical Computer Science 161, pp. 189–202.
Published: 24th August 2014.

ArXived at: http://dx.doi.org/10.4204/EPTCS.161.17 bibtex PDF

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