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16
Regular path queries on graphs with data
 In ICDT’12
"... Graph data models received much attention lately due to applications in social networks, semantic web, biological databases and other areas. Typical query languages for graph databases retrieve their topology, while actual data stored in them is usually queried using standard relational mechanisms. ..."
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Graph data models received much attention lately due to applications in social networks, semantic web, biological databases and other areas. Typical query languages for graph databases retrieve their topology, while actual data stored in them is usually queried using standard relational mechanisms. Our goal is to develop techniques that combine these two modes of querying, and give us query languages that can ask questions about both data and topology. As the basic querying mechanism we consider regular path queries, with the key difference that conditions on paths between nodes now talk not only about labels but also specify how data changes along the path. Paths that combine edge labels with data values are closely related to data words, so for stating conditions in queries, we look at several dataword formalisms developed recently. We show that many of them immediately lead to intractable data complexity for graph queries, with the notable exception of register automata, which can specify many properties of interest, and have NLOGSPACE data and PSPACE combined complexity. As register automata themselves are not easy to use in querying, we define two types of extensions of regular expressions that are more userfriendly, and develop query evaluation techniques for them. For one class, regular expressions with memory, we achieve the same bounds as for automata, and for the other class, regular expressions with equality, we also obtain tractable combined complexity of query evaluation. In addition, we show that results extends to analogs of conjunctive regular path queries.
Recursive queries on trees and data trees ∗
"... The analysis of datalog programs over relational structures has been studied in depth, most notably the problem of containment. The analysis problems that have been considered were shown to be undecidable with the exception of (i) containment of arbitrary programs in nonrecursive ones, (ii) containm ..."
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Cited by 3 (0 self)
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The analysis of datalog programs over relational structures has been studied in depth, most notably the problem of containment. The analysis problems that have been considered were shown to be undecidable with the exception of (i) containment of arbitrary programs in nonrecursive ones, (ii) containment of monadic programs, and (iii) emptiness. In this paper, we are concerned with a much less studied problem, the analysis of datalog programs over data trees. We show that the analysis of datalog programs is more complex for data trees than for arbitrary structures. In particular, we prove that the three aforementioned problems are undecidable for data trees. But in practice, data trees (e.g., XML trees) are often of bounded depth. We prove that all three problems are decidable over bounded depth data trees. Another contribution of the paper is the study of a new form of automata called pattern automata, that are essentially equivalent to linear datalog programs. We use pattern automata to show that the emptiness problem for linear monadic datalog programs with data value inequalities is decidable over arbitrary data trees. 1.
An Automata Model for Trees with Ordered Data Values
"... 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 equalit ..."
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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 ordereddata tree automata (ODTA), provide its logical characterisation, and prove that its emptiness problem is decidable in 3NEXPTIME. 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 treelike partially ordered domain, such as strings.
A decidable twoway logic on data words
"... Abstract—We study the satisfiability problem for a logic on data words. A data word is a finite word where every position carries a label from a finite alphabet and a data value from an infinite domain. The logic we consider is twoway, contains future and past modalities, which are considered as re ..."
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Abstract—We study the satisfiability problem for a logic on data words. A data word is a finite word where every position carries a label from a finite alphabet and a data value from an infinite domain. The logic we consider is twoway, contains future and past modalities, which are considered as reflexive and transitive relations, and data equality and inequality tests. This logic corresponds to the fragment of XPath with the ‘followingsiblingorself’ and ‘precedingsiblingorself ’ axes over data words. We show that this problem is decidable, EXPSPACEcomplete. This is surprising considering that with the strict (nonreflexive) navigation relations the satisfiability problem is undecidable. To prove this, we first reduce the problem to a derivation problem for an infinite transition system, and then we show how to abstract this problem into a reachability problem of a finite transition system. I.
Alternating register automata on finite data words and trees ∗
, 2010
"... Abstract. We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate oneway automata with alterna ..."
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Abstract. We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate oneway automata with alternating control over data words or trees, with one register for storing data and comparing them for equality. This is a continuation of the study started by Demri, Lazić and Jurdziński. From the standpoint of register automata models, this work aims at two objectives: (1) simplifying the existent decidability proofs for the emptiness problem for alternating register automata; and (2) exhibiting decidable extensions for these models. From the logical perspective, we show that (a) in the case of data words, satisfiability of LTL with one register and quantification over data values is decidable; and (b) the satisfiability problem for the socalled forward fragment of XPath on xml documents is decidable, even in the presence of DTDs and even of key constraints. The decidability is obtained through a reduction to the automata model introduced. This fragment contains the child, descendant, nextsibling and followingsibling axes, as well as data equality and inequality tests. 1.
Tree Regular Model Checking for LatticeBased Automata
 in "CIAA  18th International Conference on Implementation and Application of Automata
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An AutomataTheoretic Approach to the Verification of Distributed Algorithms∗
"... Abstract. We introduce an automatatheoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader). Processes have unique identifiers (pids) from an infin ..."
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Abstract. We introduce an automatatheoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader). Processes have unique identifiers (pids) from an infinite, totally ordered domain. An algorithm proceeds in synchronous rounds, each round allowing a process to perform a bounded sequence of actions such as send or receive a pid, store it in some register, and compare register contents wrt. the associated total order. An algorithm is supposed to be correct independently of the number of processes. To specify correctness properties, we introduce a logic that can reason about processes and pids. Referring to leader election, it may say that, at the end of an execution, each process stores the maximum pid in some dedicated register. Since the verification of distributed algorithms is undecidable, we propose an underapproximation technique, which bounds the number of rounds. This is an appealing approach, as the number of rounds needed by a distributed algorithm to conclude is often exponentially smaller than the number of processes. We provide an automatatheoretic solution, reducing model checking to emptiness for alternating twoway automata on words. Overall, we show that roundbounded verification of distributed algorithms over rings is PSpacecomplete.
Tree Regular Model Checking for
, 2013
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. appor t t e ch n i qu e
Static Analysis and Query Answering for Incomplete Data Trees with Constraints
"... Abstract. Data trees serve as an abstraction of XML documents: in such trees, every node comes with a label from a finite alphabet, as well as a data value from an infinite set. Incomplete data trees model XML documents with incomplete information; they may include both structural incompleteness and ..."
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Abstract. Data trees serve as an abstraction of XML documents: in such trees, every node comes with a label from a finite alphabet, as well as a data value from an infinite set. Incomplete data trees model XML documents with incomplete information; they may include both structural incompleteness and incompleteness of data. Here we study two basic problems for incomplete data trees under typical constraints such as keys and foreign keys. The first problem is consistency of specifications of incomplete data trees. We show that many of recently established results on consistency of constraints and schema descriptions can be transferred to the consistency of incomplete tree specifications without any increase in complexity. After that we examine query answering over incomplete data trees under constraints, and show that tractable bounds can be recovered under key constraints, but are lost under foreign keys. 1
Research Scientists
"... and verification of database driven systems 2 5.2. Distributed data management 3 5.3. Tree automata theory 3 ..."
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and verification of database driven systems 2 5.2. Distributed data management 3 5.3. Tree automata theory 3