Automata and Logics for Unranked and Unordered Trees

Boneva, Iovka; Talbot, Jean-Marc

doi:10.1007/978-3-540-32033-3_36

Cited by 14 publications

(30 citation statements)

References 20 publications

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“…For instance, {| d 1 : {q 1 , q 2 }, d 2 : {q 2 , q 3 } | } |= #q 1 + #q 2 = 3. This allows in general to obtain more concise automata than in case of the Presburger tree automata of [12,3] which are non-deterministic, which is to say that acceptance is based on the notion of a run that assigns a single state to each tree, even when this is done in a non-deterministic way.…”

Section: Alternating Presburger Tree Automatamentioning

confidence: 99%

“…Logics and automata for unordered trees were studied in the last twenty years mostly for querying XML documents [12,3,18] and more recently for querying NOSQL databases [1]. They were already studied earlier, for modeling feature structures in computational linguistics [15] and records in programming languages [16,9,10].…”

Section: Introductionmentioning

confidence: 99%

“…at most one file matching * ".tex" whose content matches "\documentclass"*. This property can be checked by formulae from the Counting MSO fragment of Presburger MSO, but extended with regular expressions for matching data values: #( * ".tex" : {"\documentclass" * : {}}) = 1 Alternatively, any formula of Presburger MSO can be expressed by a Presburger tree automaton [12,3], if extended with regular expressions for matching data values.…”

Section: Introductionmentioning

confidence: 99%

“…The existing notions of tree automata for unordered trees are well-investigated concerning expressiveness (either Counting or Presburger MSO: CMSO or PMSO) [12,3], and have the advantage that membership can be tested in PTIME. When it comes to static analysis problems such as satisfiability, inclusion, or equivalence checking, they all lack a proper notion of determinism, which makes it difficult to distinguish subclasses of automata for which these problems can be solved efficiently.…”

Section: Introductionmentioning

confidence: 99%

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Deterministic Automata for Unordered Trees

Boiret

Hugot²,

Niehren³

et al. 2014

Electron. Proc. Theor. Comput. Sci.

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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 Counting MSO.

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Section: Alternating Presburger Tree Automatamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Deterministic Automata for Unordered Trees

Boiret

Hugot²,

Niehren³

et al. 2014

Electron. Proc. Theor. Comput. Sci.

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show abstract

“…In order to query XML documents with arithmetical and regular constraints, logical and automata-based formalisms have been recently introduced [42,15,8,35,41] leading to various expressiveness and complexity results about logics and specialized tree automata. As usual, XML documents are viewed as labeled, unranked ordered trees.…”

Section: Logics For Xml Documentsmentioning

confidence: 99%

Complexity of modal logics with Presburger constraints

Demri¹,

Lugiez²

2010

Journal of Applied Logic

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We introduce the Extended Modal Logic EML with regularity constraints and full Presburger constraints on the number of children that generalize graded modalities, also known as number restrictions in description logics. We show that EML satisfiability is only pspacecomplete by designing a Ladner-like algorithm. This extends a well-known and nontrivial pspace upper bound for graded modal logic. Furthermore, we provide a detailed comparison with logics that contain Presburger constraints and that are dedicated to query XML documents. As an application, we provide a logarithmic space reduction from a variant of Sheaves Logic SL into EML that allows us to establish that its satisfiability problem is also pspace-complete, significantly improving the best known upper bound.

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Monotone AC-Tree Automata

Ohsaki

Talbot

Tison

et al. 2005

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. We consider several questions about monotone AC-tree automata, a class of equational tree automata whose transition rules correspond to rules in Kuroda normal form of context-sensitive grammars. Whereas it has been proved that this class has a decision procedure to determine if, given a monotone AC-tree automaton, it accepts no terms, other important decidability or complexity results have not been well-investigated yet. In the paper, we prove that the membership problem for monotone AC-tree automata is PSPACE-complete. We then study the expressiveness of monotone AC-tree automata: precisely, we prove that the family of AC-regular tree languages is strictly subsumed in that of AC-monotone tree languages. The proof technique used in obtaining the above result yields the answers to two different questions, specifically that the family of monotone AC-tree languages is not closed under complementation, and that the inclusion problem for monotone AC-tree automata is undecidable.

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Automata and Logics for Unranked and Unordered Trees

Cited by 14 publications

References 20 publications

Deterministic Automata for Unordered Trees

Deterministic Automata for Unordered Trees

Complexity of modal logics with Presburger constraints

Monotone AC-Tree Automata

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