Results 1  10
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35
An extension of data automata that captures XPath
, 2010
"... Abstract—We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automatatheoretic approach may be applied to answer decidability and expressibility questions for XPath. Finally, ..."
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Abstract—We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automatatheoretic approach may be applied to answer decidability and expressibility questions for XPath. Finally, we use the newly introduced automata as a common framework to classify existing automata on data words and trees, including data automata, register automata and alternating register automata. KeywordsRegular XPath, data automata, register automata. I.
Efficient Reasoning about Data Trees via Integer Linear Programming
, 2011
"... Data trees provide a standard abstraction of XML documents with data values: they are trees whose nodes, in addition to the usual labels, can carry labels from an infinite alphabet (data). Therefore, one is interested in decidable formalisms for reasoning about data trees. While some are known – su ..."
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Cited by 11 (2 self)
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Data trees provide a standard abstraction of XML documents with data values: they are trees whose nodes, in addition to the usual labels, can carry labels from an infinite alphabet (data). Therefore, one is interested in decidable formalisms for reasoning about data trees. While some are known – such as the twovariable logic – they tend to be of very high complexity, and most decidability proofs are highly nontrivial. We are therefore interested in reasonable complexity formalisms as well as better techniques for proving decidability. Here we show that many decidable formalisms for data trees are subsumed – fully or partially – by the power of tree automata together with set constraints and linear constraints on cardinalities of various sets of data values. All these constraints can be translated into instances of integer linear programming, giving us an NP bound on the complexity of the reasoning tasks. We prove that this bound, as well as the key encoding technique, remain very robust, and allow the addition of features such as counting of paths and patterns, and even a concise encoding of constraints, without increasing the complexity. We also relate our results to several reasoning tasks over XML documents, such as satisfiability of schemas and data dependencies and satisfiability of the twovariable logic.
Graph reachability and pebble automata over infinite alphabets
 In LICS’09
"... Abstract—We study the graph reachability problem as a language over an infinite alphabet. Namely, we view a word of even length a0b0 ···anbn over an infinite alphabet as a directed graph with the symbols that appear in a0b0 ···anbn as the vertices and (a0,b0),...,(an,bn) as the edges. We prove that ..."
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Abstract—We study the graph reachability problem as a language over an infinite alphabet. Namely, we view a word of even length a0b0 ···anbn over an infinite alphabet as a directed graph with the symbols that appear in a0b0 ···anbn as the vertices and (a0,b0),...,(an,bn) as the edges. We prove that for any positive integer k, k pebbles are sufficient for recognizing the existence of a path of length 2 k − 1 from the vertex a0 to the vertex bn, but are not sufficient for recognizing the existence of a path of length 2 k+1 −2 from the vertex a0 to the vertex bn. Based on this result, we establish a number of relations among some classes of languages over infinite alphabets. KeywordsGraph reachability; pebble automata; infinite alphabets I.
Node Selection Query Languages for Trees
"... The study of nodeselection query languages for (finite) trees has been a major topic in the recent research on query languages for Web documents. On one hand, there has been an extensive study of XPath and its various extensions. On the other hand, query languages based on classical logics, such as ..."
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The study of nodeselection query languages for (finite) trees has been a major topic in the recent research on query languages for Web documents. On one hand, there has been an extensive study of XPath and its various extensions. On the other hand, query languages based on classical logics, such as firstorder logic (FO) or monadic secondorder logic (MSO), have been considered. Results in this area typically relate an Xpathbased language to a classical logic. What has yet to emerge is an XPathrelated language that is expressive as MSO, and at the same time enjoys the computational properties of XPath, which are linear query evaluation and exponential querycontainment test. In this paper we propose µXPath, which is the alternationfree fragment of XPath extended with fixpoint operators. Using twoway alternating automata, we show that this language does combine desired expressiveness and computational properties, placing it as an attractive candidate as the definite query language for trees.
A Fresh Approach to Learning Register Automata
, 2013
"... This paper provides an Angluinstyle learning algorithm for a class of register automata supporting the notion of fresh data values. More specifically, we introduce session automata which are well suited for modeling protocols in which sessions using fresh values are of major interest, like in secu ..."
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This paper provides an Angluinstyle learning algorithm for a class of register automata supporting the notion of fresh data values. More specifically, we introduce session automata which are well suited for modeling protocols in which sessions using fresh values are of major interest, like in security protocols or adhoc networks. We show that session automata (i) have an expressiveness partly extending, partly reducing that of register automata, (ii) admit a symbolic regular representation, and (iii) have a decidable equivalence and modelchecking problem (unlike register automata). Using these results, we establish a learning algorithm to infer session automata through membership and equivalence queries. Finally, we strengthen the robustness of our automaton by its characterization in monadic secondorder logic.
Ordered navigation on multiattributed data words
 In Proc. of CONCUR’14, volume 8704 of LNCS
, 2014
"... Abstract. We study temporal logics and automata on multiattributed data words. Recently, BDLTL was introduced as a temporal logic on data words extending LTL by navigation along positions of single data values. As allowing for navigation wrt. tuples of data values renders the logic undecidable, we ..."
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Abstract. We study temporal logics and automata on multiattributed data words. Recently, BDLTL was introduced as a temporal logic on data words extending LTL by navigation along positions of single data values. As allowing for navigation wrt. tuples of data values renders the logic undecidable, we introduce NDLTL, an extension of BDLTL by a restricted form of tuplenavigation. While complete NDLTL is still undecidable, the two natural fragments allowing for either future or past navigation along data values are shown to be Ackermannhard, yet decidability is obtained by reduction to nested multicounter systems. To this end, we introduce and study nested variants of data automata as an intermediate model simplifying the constructions. To complement these results we show that imposing the same restrictions on BDLTL yields two 2ExpSpacecomplete fragments while satisfiability for the full logic is known to be as hard as reachability in Petri nets. 1
Satisfiability for twovariable logic with two successor relations on finite linear orders
 CoRR
"... We study the finite satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders. We show that the problem is decidable in NExpTime. 1. ..."
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We study the finite satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders. We show that the problem is decidable in NExpTime. 1.
Walking on Data Words
, 2013
"... We see data words as sequences of letters with additional edges that connect pairs of positions carrying the same data value. We consider a natural model of automaton walking on data words, called Data Walking Automaton, and study its closure properties, expressiveness, and the complexity of parad ..."
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We see data words as sequences of letters with additional edges that connect pairs of positions carrying the same data value. We consider a natural model of automaton walking on data words, called Data Walking Automaton, and study its closure properties, expressiveness, and the complexity of paradigmatic problems. We prove that deterministic DWA are strictly included in nondeterministic DWA, that the former subclass is closed under all boolean operations, and that the latter class enjoys a decidable containment problem.
Walk logic as a framework for path query languages on graph databases
 In Proceedings of the 16th International Conference on Database Theory, ICDT ’13
, 2013
"... ABSTRACT Motivated by the current interest in languages for expressing path queries to graph databases, this paper proposes to investigate Walk Logic (WL): the extension of firstorder logic on finite graphs with the possibility to explicitly quantify over walks. WL can serve as a unifying framewor ..."
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ABSTRACT Motivated by the current interest in languages for expressing path queries to graph databases, this paper proposes to investigate Walk Logic (WL): the extension of firstorder logic on finite graphs with the possibility to explicitly quantify over walks. WL can serve as a unifying framework for path query languages. To support this claim, WL is compared in expressive power with various established query languages for graphs, such as firstorder logic extended with reachability; the monadic secondorder logic of graphs; hybrid computation tree logic; and regular path queries. WL also serves as a framework to investigate the following natural questions: Is quantifying over walks more powerful than quantifying over paths (walks without repeating nodes) only? Is quantifying over infinite walks more powerful than quantifying over finite walks only? WL model checking is decidable, but determining the precise complexity remains an open problem.