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Vincent Hugot

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3 papers

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I&C Journal 2017 Journal Article

Automata for unordered trees

Adrien Boiret
Vincent Hugot
Joachim Niehren
Ralf Treinen

We present a framework for defining automata for unordered data trees that is parametrised by the way in which multisets of children nodes are described. Presburger tree automata and alternating Presburger tree automata are particular instances. We establish the usual equivalence in expressiveness of tree automata and MSO for our framework. We then investigate subclasses of automata for unordered trees for which testing language equivalence is in P-time. Starting from automata in our framework that describe multisets of children by finite automata, we propose two approaches to do this deterministically. We show that confluent horizontal evaluation leads to polynomial-time emptiness and universality, but coNP-complete emptiness and intersection. 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 Counting Mso.

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GandALF Workshop 2014 Workshop Paper

Deterministic Automata for Unordered Trees

Adrien Boiret
Vincent Hugot
Joachim Niehren
Ralf Treinen

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.

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TCS Journal 2012 Journal Article

Loops and overloops for Tree-Walking Automata

Pierre-Cyrille Héam
Vincent Hugot
Olga Kouchnarenko

Tree-Walking Automata (TWA) have lately received renewed interest thanks to their tight connection to XML. This paper introduces the notion of tree overloops, which is closely related to tree loops, and investigates the use of both for the following common operations on TWA: testing membership, transformation into a Bottom-Up Tree Automaton (BUTA), and testing emptiness. Notably, we argue that the transformation into a BUTA is slightly less straightforward than was previously assumed, show that using overloops yields much smaller BUTA in the deterministic case, and provide a polynomial over-approximation of this construction which detects emptiness with surprising accuracy against randomly generated TWA.

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