On XPath with transitive axes and data tests

Figueira, Diego

doi:10.1145/2463664.2463675

Cited by 9 publications

(7 citation statements)

References 22 publications

(32 reference statements)

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“…In fact, both SAT-XPath(→ * ) and SAT-XPath(→ * , * ←) are ExpSpace-complete [Fig11]. What is more, this good behavior extends also to trees, as SAT-XPath(→ * , * ←, ↓ * ) is also of elementary complexity [Fig13] (somewhere between ExpSpace and 3ExpSpace).…”

Section: Transitive Axesmentioning

confidence: 93%

Satisfiability of Xpath on data trees

Figueira

2018

ACM SIGLOG News

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This is a survey on the satisfiability problem for XPath on data trees. Data trees are finite trees whose every node carries a label from a finite alphabet and a data value from an infinite domain. XPath is an expressive node selecting language for XML documents, which can be abstracted as data trees. Its satisfiability problem is in general undecidable. However, various fragments of XPath have decidable satisfiability problem, these are fragments defined in terms of the navigational axes which are allowed. We explore the state of the art in terms of decidability and discuss briefly some of the algorithmic techniques involved.

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Section: Transitive Axesmentioning

confidence: 93%

Satisfiability of Xpath on data trees

Figueira

2018

ACM SIGLOG News

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“…Related work. This paper combines work on unordered trees and the associated automata and logics, as in [4,5,6], with questions about data values that are closely related to problems studied in the databases community for register automata, first-order logic, and XPath, [16,19], among others. The upshot of the existing work is that, in the ordered case, even the mere ability to express equality between data values renders very simple logics intractable or undecidable.…”

Section: Filetex Dirmentioning

confidence: 99%

Logics for unordered trees with data constraints

Boiret

Hugot

Niehren³

et al. 2019

Journal of Computer and System Sciences

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We study monadic second-order logics with counting constraints (CMso) for unordered data trees. Our objective is to enhance this logic with data constraints for comparing string data values. Comparisons between data values at arbitrary positions of a data tree quickly lead to undecidability. Therefore, we restrict ourselves to comparing sibling data values of unordered trees. But even in this case CMso remains undecidable when allowing for data comparisons that can check the equality of string factors. However, for more restricted data constraints that can only check the equality of string prefixes, it becomes decidable. This decidability result is obtained by reduction to WSkS. Furthermore, we exhibit a restricted class of constraints which can be used in transitions of tree automata, resulting in a model with tractable complexity, which can be extended with structural equality tests between siblings. This efficient restriction is relevant to applications such as checking well-formedness properties of file system trees. more general graphs or structures is undecidable. In this paper, we will consider Mso over unordered data trees. This means that we annotate the elements of the data tree with strings or other data values from an infinite alphabet. Depending on which relations on data values are supported, unordered data trees subsume graphs, so that Mso becomes undecidable again.Unordered data trees are a versatile data structure that is of interest in various domains of computer science. More recently, they were used as data models of semi-structured databases, such as for NoSql databases [3] or for Xml databases [4,5,6]. Here, Mso can be used both as a query language and as a schema language. Unordered data trees also have a long history for modeling syntactic structures in computational linguistics [7] and records in programming languages [8,9,10]. The unordered data trees in this context were called feature trees and the corresponding logics feature logics [11,12]. Our own motivation is to model file systems, i.e. trees representing directories, files names, their contents etc.Yet, so far, Mso for unordered trees has been studied without data, that is over finite alphabets. The two main variants of Mso for unordered trees that were proposed are Presburger Mso and Counting Mso [4, 5, 6]. Both logics were proven decidable by reduction to corresponding notions of automata for unranked trees. The weaker logic, Counting Mso or CMso for short, is considered a canonical language for characterising recognizable sets, and is actually equivalent to Mso in the case of ordered trees or words [13]. In this present paper, we generalize CMso to unordered data trees with arbitrary ranks, and study the expressiveness of the resulting logics.The most general extension of CMso would enable comparisons of data values between arbitrary locations, but this immediately leads to undecidability. Indeed even Mso on data words with equality tests between the data values of arbitrary positions is undecidable [14] since it can be reduce...

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“…What is more, this good behavior extends also to trees, as SAT-XPath(! ⇤ , ⇤ , # ⇤ ) is also of elementary complexity [Figueira 2013] (somewhere between EXPSPACE and 3EXPSPACE).…”

Section: Transitive Axesmentioning

confidence: 99%

Stochastic process algebras and their markovian semantics

Hillston

2018

ACM SIGLOG News

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There is a long tradition of quantitative modelling in computer and telecommunication systems for performance evaluation and dependability analysis, dating back to the early work of Erlang on telephone exchanges at the beginning of twentieth century [Erlang 1917]. These models are typically stochastic, not because the behaviour of the system under study is inherently random, but because the models usually abstract from data and because interactions with humans are often intrinsic to the system, and both of these give rise to apparently stochastic behaviour. Whilst systems remained of moderate size, models could readily be hand-crafted, and results such as Little's Law were derived and widely-used, for example to optimise job shops [Little 1961]. Much work, like Little's Law, was based on a queueing abstraction, treating the resource in the system as the server of a queue, with users following an appropriate queueing discipline before gaining access to the resource. The more contention there is for the resource, the longer jobs are likely to spend in the queue waiting for access. The queueing paradigm is based on an essentially sequential view of computation and communication, with jobs flowing between resources, completing one task after another. Nevertheless it functioned extremely well until the 1980s, and for many people performance modelling was synonymous with queueing theory. However, the arrival of distributed systems that allowed jobs to access more than one resource at once, and multicast and broadcast communication, broke the assumptions of basic queueing theory making it much harder to carry out quantitative analysis of stochastic systems in order to predict non-functional properties such as performance, availability, reliability and dependability.

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On XPath with transitive axes and data tests

Cited by 9 publications

References 22 publications

Satisfiability of Xpath on data trees

Satisfiability of Xpath on data trees

Logics for unordered trees with data constraints

Stochastic process algebras and their markovian semantics

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