A Tree Logic with Graded Paths and Nominals

Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node cardinality constraints occur along a path in a tree. We present a logic capable of expressing deep counting along paths which may include arbitrary recursive forward and backward navigation. The counting extensions can be seen as a generalization of graded modalities that count immediate successor nodes. While the combination of graded modalities, nominals, and inverse modalities yields undecidable logics over graphs, we show that these features can be combined in a tree logic decidable in exponential time

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

05061 Abstracts Collection -- Foundations of Semistructured Data

From 06.02.05 to 11.02.05, the Dagstuhl Seminar 05061 ``Foundations of Semistructured Data\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

The DSD Schema Language and its Applications

XML (eXtensible Markup Language), a linear syntax for trees, has gathered a remarkable amount of interest in industry. The acceptance of XML opens new venues for the application of formal methods such as specification of abstract syntax tree sets and tree transformations. A user domain may be specified as a set of trees. For example, XHTML is a user domain corresponding to the set of XML documents that make sense asHTML. A notation for defining such a set of XML trees is called a schema language. We believe that a useful schema notation must identify most of the syntacticrequirements that the documents in the user domain follow; allow efficient parsing; be readable to the user; allow a declarative default notation `a la CSS; and bemodular and extensible to support evolving classes of XML documents. In the present paper, we give a tutorial introduction to the DSD (Document Structure Description) notation as our bid on how to meet these requirements. TheDSD notation was inspired by industrial needs, and we show how DSDs help manage aspects of complex XML software through a case study about interactive voiceresponse systems (automated telephone answering systems, where input is through the telephone keypad or speech recognition). The expressiveness of DSDs goes beyond the DTD schema concept that is alreadypart of XML. We advocate the use of nonterminals in a top-down manner, coupled with boolean logic and regular expressions to describe how constraints on tree nodes depend on their context. We also support a general, declarative mechanism for inserting default elements and attributes that is reminiscent of CascadingStyle Sheets (CSS), a way of manipulating formatting instructions in HTML that is built into all modern browsers. Finally, we include a simple technique for evolving DSDs through selective redefinitions. DSDs are in many ways much more expressive than XML Schema (the schema language proposed by the W3C), but their syntactic and semantic definition in English is only 1/8th the size. Also, the DSD notation is self-describable: the syntax of legal DSD documents and all static semantic requirements can be captured in a DSD document, called the meta-DSD

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

Deterministic Automata for Unordered Trees

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.Comment: In Proceedings GandALF 2014, arXiv:1408.556