Transformations Between Different Types of Unranked Bottom-Up Tree Automata

We consider the representational state complexity of unranked tree automata. The bottom-up computation of an unranked tree automaton may be either deterministic or nondeterministic, and further variants arise depending on whether the horizontal string languages defining the transitions are represented by a DFA or an NFA. Also, we consider for unranked tree automata the alternative syntactic definition of determinism introduced by Cristau et al. (FCT'05, Lect. Notes Comput. Sci. 3623, pp. 68-79). We establish upper and lower bounds for the state complexity of conversions between different types of unranked tree automata.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Operational State Complexity of Deterministic Unranked Tree Automata

We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic tree automata are obtained. For tree concatenation we establish a tight upper bound that is of a different order than the known state complexity of concatenation of regular string languages. We show that (n+1) ( (m+1)2^n-2^(n-1) )-1 vertical states are sufficient, and necessary in the worst case, to recognize the concatenation of tree languages recognized by (strongly or weakly) deterministic automata with, respectively, m and n vertical states.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Logics for Unranked Trees: An Overview

Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees

Rewrite Closure and CF Hedge Automata

We introduce an extension of hedge automata called bidimensional context-free hedge automata. The class of unranked ordered tree languages they recognize is shown to be preserved by rewrite closure with inverse-monadic rules. We also extend the parameterized rewriting rules used for modeling the W3C XQuery Update Facility in previous works, by the possibility to insert a new parent node above a given node. We show that the rewrite closure of hedge automata languages with these extended rewriting systems are context-free hedge languages

Minimizing Tree Automata for Unranked Trees

International audienceAutomata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. We start with the unranked tree automata (UTAs) that are standard in database theory, assuming bottom-up determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal UTAs in that class are not unique and that minimization is NP-hard. We then study more recent automata classes that do allow for polynomial time minimization. Among those, we show that bottom-up deterministic stepwise tree automata yield the most succinct representations

On Probability Distributions for Trees: Representations, Inference and Learning

We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied class of tree series is the class of rational (or recognizable) tree series which can be defined either in an algebraic way or by means of multiplicity tree automata. We argue that the algebraic representation is very convenient to model probability distributions over a free algebra of trees. First, as in the string case, the algebraic representation allows to design learning algorithms for the whole class of probability distributions defined by rational tree series. Note that learning algorithms for rational tree series correspond to learning algorithms for weighted tree automata where both the structure and the weights are learned. Second, the algebraic representation can be easily extended to deal with unranked trees (like XML trees where a symbol may have an unbounded number of children). Both properties are particularly relevant for applications: nondeterministic automata are required for the inference problem to be relevant (recall that Hidden Markov Models are equivalent to nondeterministic string automata); nowadays applications for Web Information Extraction, Web Services and document processing consider unranked trees

Unranked Tree Rewriting and Effective Closures of Languages

International audienceWe consider rewriting systems for unranked ordered trees, where the number of chil- dren of a node is not determined by its label, and is not a priori bounded. The rewriting systems are defined such that variables in the rewrite rules can be substituted by hedges (sequences of trees) instead of just trees. Consequently, this notion of rewriting subsumes both standard term rewriting and word rewriting.We present some properties of preservation for classes of unranked tree languages, including hedge automata languages and various context-free extensions. Finally, ap- plications to static type checking for XML transformations and to the verification of read/write access control policies for XML updates are mentioned

Advances and applications of automata on words and trees : executive summary

Seminar: 10501 - Advances and Applications of Automata on Words and Trees. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail

A Direct Translation from XPath to Nondeterministic Automata

Abstract. Since navigational aspects of XPath correspond to first-order definability, it has been proposed to use the analogy with the very successful technique of translating LTL into automata, and produce efficient translations of XPath queries into automata on unranked trees. These translations can then be used for a variety of reasoning tasks such as XPath consistency, or optimization, under XML schema constraints. In the verification scenarios, translations into both nondeterministic and alternating automata are used. But while a direct translation from XPath into alternating automata is known, only an indirect translation into nondeterministic automata- going via intermediate logics- exists. A direct translation is desirable as most XML specifications have particularly nice translations into nondeterministic automata and it is natural to use such automata to reason about XPath and schemas. The goal of the paper is to produce such a direct translation of XPath into nondeterministic automata.