A Decidable Temporal Logic of Repeating Values

Demri, Stéphane; D’Souza, Deepak; Gascon, Régis

doi:10.1007/978-3-540-72734-7_13

Cited by 17 publications

(20 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Interest in such structures with data springs due to their connection to XML [1], [2], [5], [12], [17], [18], [32], as well as system specifications [9], [13], [36], where many properties simply cannot be captured by finite alphabets. This has motivated various works on data words [3], [8], [14], [22], [25], [33], as well as on data trees [4], [6], [20], [21], [24].…”

Section: Introductionmentioning

confidence: 99%

An Automata Model for Trees with Ordered Data Values

Tan

2012

2012 27th Annual IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

Data trees are trees in which each node, besides carrying a label from a finite alphabet, also carries a data value from an infinite domain. They have been used as an abstraction model for reasoning tasks on XML and verification. However, most existing approaches consider the case where only equality test can be performed on the data values.In this paper we study data trees in which the data values come from a linearly ordered domain, and in addition to equality test, we can test whether the data value in a node is greater than the one in another node. We introduce an automata model for them which we call ordered-data tree automata (ODTA), provide its logical characterisation, and prove that its emptiness problem is decidable in 3-NEXPTIME. We also show that the twovariable logic on unranked trees, studied by Bojanczyk, Muscholl, Schwentick and Segoufin in 2009, corresponds precisely to a special subclass of this automata model.Then we define a slightly weaker version of ODTA, which we call weak ODTA, and provide its logical characterisation. The complexity of the emptiness problem drops to NP. However, a number of existing formalisms and models studied in the literature can be captured already by weak ODTA. We also show that the definition of ODTA can be easily modified, to the case where the data values come from a tree-like partially ordered domain, such as strings.

show abstract

Section: Introductionmentioning

confidence: 99%

An Automata Model for Trees with Ordered Data Values

Tan

2012

2012 27th Annual IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

show abstract

“…Related work. The most closely related work is the one originated by Demri et al in [5,6] and pursued in [7]. These works study the satisfiability problem for temporal logics on data words, extended with the ability to test whether a data value is repeated in the past/future.…”

Section: Contributions the Main Contributions Are The Followingmentioning

confidence: 99%

“…5 The idea is that ⊕(U, V ) holding at x means that there must be a data value appearing in the subtree at x under all the variables of V (possibly at different nodes), which is equal to the u-attribute of the k-ancestor of x, for every u ∈ U . On the other hand, (U, V ) holding at x means that the data value of the U -attributes of x (which are all the same) do no not appear in any i-ancestor of x (i ≤ k), and they will appear in the future with attributes V .…”

Section: Proof (Idea)mentioning

confidence: 99%

Logics of Repeating Values on Data Trees and Branching Counter Systems

Abriola

Figueira

2017

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We study connections between the satisfiability problem for logics on data trees and Branching Vector Addition Systems (BVAS). We consider a natural temporal logic of "repeating values" (LRV) featuring an operator which tests whether a data value in the current node is repeated in some descendant node. On the one hand, we show that the satisfiability of a restricted version of LRV on ranked data trees can be reduced to the coverability problem for Branching Vector Addition Systems. This immediately gives elementary upper bounds for its satisfiability problem, showing that restricted LRV behaves much better than downward-XPath, which has a non-primitiverecursive satisfiability problem. On the other hand, satisfiability for LRV is shown to be reducible to the coverability for a novel branching model we introduce here, called Merging VASS (MVASS). MVASS is an extension of Branching Vector Addition Systems with States (BVASS) allowing richer merging operations of the vectors. We show that the control-state reachability for MVASS, as well as its bottom-up coverability, are in 3ExpTime. This work can be seen as a natural continuation of the work initiated by Demri, D'Souza and Gascon for the case of data words, this time considering branching structures and counter systems, although, as we show, in the case of data trees more powerful models are needed to encode satisfiability.

show abstract

“…Interest in such structures with data springs due to their connection to XML [Alon et al 2003;Arenas et al 2008;Björklund et al 2008;David et al 2012;Fan and Libkin 2002;Figueira 2009;Neven 2002], as well as system specifications [Bouyer et al 2001;Demri et al 2007;Segoufin and Torunczyk 2011], where many properties simply cannot be captured by finite alphabets. This has motivated various works on data words [Benedikt et al 2010;Bojanczyk et al 11a;Demri and Lazić 2009;Grumberg et al 2010;Kaminski and Francez 1994;Neven et al 2004], as well as…”

Section: Introductionmentioning

confidence: 99%

Extending two-variable logic on data trees with order on data values and its automata

Tan

2014

ACM Trans. Comput. Logic

View full text Add to dashboard Cite

a node is greater than the one in another node. We introduce an automata model for them which we call ordered-data tree automata (ODTA), provide its logical characterisation, and prove that its non-emptiness problem is decidable in 3-NExpTime. We also show that the two-variable logic on unranked data trees, studied by Bojanczyk, Muscholl, Schwentick and Segoufin in 2009, corresponds precisely to a special subclass of this automata model.Then we define a slightly weaker version of ODTA, which we call weak ODTA, and provide its logical characterisation. The complexity of the non-emptiness problem drops to NP. However, a number of existing formalisms and models studied in the literature can be captured already by weak ODTA. We also show that the definition of ODTA can be easily modified, to the case where the data values come from a tree-like partially ordered domain, such as strings.

show abstract

A Decidable Temporal Logic of Repeating Values

Cited by 17 publications

References 20 publications

An Automata Model for Trees with Ordered Data Values

An Automata Model for Trees with Ordered Data Values

Logics of Repeating Values on Data Trees and Branching Counter Systems

Extending two-variable logic on data trees with order on data values and its automata

Contact Info

Product

Resources

About