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Querying graph databases with XPath
, 2013
"... General Terms XPath plays a prominent role as an XML navigational language due to several factors, including its ability to express queries of interest, its close connection to yardstick database query languages (e.g., firstorder logic), and the low complexity of query evaluation for many fragments ..."
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General Terms XPath plays a prominent role as an XML navigational language due to several factors, including its ability to express queries of interest, its close connection to yardstick database query languages (e.g., firstorder logic), and the low complexity of query evaluation for many fragments. Another common database model — graph databases — also requires a heavy use of navigation in queries; yet it largely adopts a different approach to querying, relying on reachability patterns expressed with regular constraints. Our goal here is to investigate the behavior and applicability of XPathlike languages for querying graph databases, concentrating on their expressiveness and complexity of query evaluation. We are particularly interested in a model of graph data that combines navigation through graphs with querying data held in the nodes, such as, for example, in a social network scenario. As navigational languages, we use analogs of core and regular XPath and augment them with various tests on data values. We relate these languages to firstorder logic, its transitive closure extensions, and finitevariable fragments thereof, proving several capture results. In addition, we describe their relative expressive power. We then show that they behave very well computationally: they have a lowdegree polynomial combined complexity, which becomes linear for several fragments. Furthermore, we introduce new types of tests for XPath languages that let them capture firstorder logic with data comparisons and prove that the low complexity bounds continue to apply to such extended languages. Therefore, XPathlike languages seem to be very wellsuited to query graphs.
COMPLEXITY HIERARCHIES BEYOND ELEMENTARY
, 2013
"... We introduce a hierarchy of fastgrowing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a nonelementary complexity, which occur naturally in logic, combinatorics, formal ..."
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Cited by 11 (4 self)
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We introduce a hierarchy of fastgrowing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a nonelementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond.
TriAL for RDF: Adapting Graph Query Languages for RDF Data
"... Querying RDF data is viewed as one of the main applications of graph query languages, and yet the standard model of graph databases – essentially labeled graphs – is different from the triplesbased model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natu ..."
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Cited by 8 (3 self)
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Querying RDF data is viewed as one of the main applications of graph query languages, and yet the standard model of graph databases – essentially labeled graphs – is different from the triplesbased model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natural ones are bound to lose somefunctionalitywhenused inconjunctionwith graph query languages. The solution is to work directly with triples, but then many properties taken for granted in the graphdatabasecontext(e.g., reachability)losetheir natural meaning. Our goal is to introduce languages that work directly over triples and are closed, i.e., they produce sets of triples, ratherthan graphs. Our basiclanguageis called TriAL, or Triple Algebra: it guarantees closure properties by replacing the product with a family of join operations. We extend TriAL with recursion, and explain why such an extension is more intricate for triples than for graphs. We present a declarative language, namely a fragment of datalog, capturing the recursive algebra. For both languages, the combined complexity of query evaluation is given by lowdegree polynomials. We compare our languages with relational languages, such as finitevariable logics, and previously studied graph query languages such as adaptations of XPath, regular path queries, and nested regular expressions; many of these languages are subsumed by the recursive triple algebra. We also provide examples of the usefulness of TriAL in querying graph, RDF, and social networks data.
GRAPH LOGICS WITH RATIONAL RELATIONS
"... Abstract. We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular ..."
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Abstract. We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword or subsequence. Evaluating formulae in such extended graph logics boils down to checking nonemptiness of the intersection of rational relations with regular or recognizable relations (or, more generally, to the generalized intersection problem, asking whether some projections of a regular relation have a nonempty intersection with a given rational relation). We prove that for several basic and commonly used rational relations, the intersection problem with regular relations is either undecidable (e.g., for subword or suffix, and some generalizations), or decidable with nonprimitiverecursive complexity (e.g., for subsequence and its generalizations). These results are used to rule out many classes of graph logics that freely combine regular and rational relations, as well as to provide the simplest problem related to verifying lossy channel systems that has nonprimitiverecursive complexity. We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classifies them into either efficiently checkable or undecidable cases. We also give examples of rational relations for which such logics are decidable even without syntactic restrictions.
Spanners: A Formal Framework for Information Extraction
, 2013
"... An intrinsic part of information extraction is the creation and manipulation of relations extracted from text. In this paper, we develop a foundational framework where the central construct is what we call a spanner. A spanner maps an input string into relations over the spans (intervals specified b ..."
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An intrinsic part of information extraction is the creation and manipulation of relations extracted from text. In this paper, we develop a foundational framework where the central construct is what we call a spanner. A spanner maps an input string into relations over the spans (intervals specified by bounding indices) of the string. The focus of this paper is on the representation of spanners. Conceptually, there are two kinds of such representations. Spanners defined in a primitive representation extract relations directly from the input string; those defined in an algebra apply algebraic operations to the primitively represented spanners. This framework is driven by SystemT, an IBM commercial product for text analysis, where the primitive representation is that of regular expressions with capture variables. We define additional types of primitive spanner representations by means of two kinds of automata that assign spans to variables. We prove that the first kind has the same expressive power as regular expressions with capture variables; the second kind expresses precisely the algebra of the regular spanners—the closure of the first kind under standard relational operators. The core spanners extend the regular ones by stringequality selection (an extension used in SystemT). We give some fundamental results on the expressiveness of regular and core spanners. As an example, we prove that regular spanners are closed under difference (and complement), but core spanners are not. Finally, we establish connections with related notions in the literature.
The Power of WellStructured Systems
"... Wellstructured systems, aka WSTS, are computational models where the set of possible configurations is equipped with a wellquasiordering which is compatible with the transition relation between configurations. This structure supports generic decidability results that are important in verificatio ..."
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Wellstructured systems, aka WSTS, are computational models where the set of possible configurations is equipped with a wellquasiordering which is compatible with the transition relation between configurations. This structure supports generic decidability results that are important in verification and several other fields. This paper recalls the basic theory underlying wellstructured systems and shows how two classic decision algorithms can be formulated as an exhaustive search for some “bad ” sequences. This lets us describe new powerful techniques for the complexity analysis of WSTS algorithms. Recently, these techniques have been successful in precisely characterizing the power, in a complexitytheoretical sense, of several important WSTS models like unreliable channel systems, monotonic counter machines, or networks of timed systems.
The Parametric OrdinalRecursive Complexity of Post Embedding Problems
, 2012
"... Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiplyrecursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) an ..."
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Cited by 3 (2 self)
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Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiplyrecursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.
Conjunctive ContextFree Path Queries
, 2014
"... In graph query languages, regular expressions are commonly used to specify the labeling of paths. A natural step in increasing the expressive power of these query languages is replacing regular expressions by contextfree grammars. With the Conjunctive ContextFree Path Queries (CCFPQ) we introduce ..."
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In graph query languages, regular expressions are commonly used to specify the labeling of paths. A natural step in increasing the expressive power of these query languages is replacing regular expressions by contextfree grammars. With the Conjunctive ContextFree Path Queries (CCFPQ) we introduce such a language based on the wellknown Conjunctive Regular Path Queries (CRPQ). First, we show that query evaluation of CCFPQ has polynomial time data complexity. Secondly, we look at the generalization of regular expressions, as used in CRPQ, to regular relations and show how similar generalizations can be applied to contextfree grammars, as used in CCFPQ. Thirdly, we investigate the relations between the expressive power of CRPQ, CCFPQ, and their generalizations. In several cases we show that replacing regular expressions by contextfree grammars does increase expressive power. Finally, we look at including contextfree grammars in more powerful logics than conjunctive queries. We do so by adding negation and provide expressivity relations between the obtained languages.
Querying Graph Databases with XPath General Terms
"... ABSTRACT XPath plays a prominent role as an XML navigational language due to several factors, including its ability to express queries of interest, its close connection to yardstick database query languages (e.g., firstorder logic), and the low complexity of query evaluation for many fragments. An ..."
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ABSTRACT XPath plays a prominent role as an XML navigational language due to several factors, including its ability to express queries of interest, its close connection to yardstick database query languages (e.g., firstorder logic), and the low complexity of query evaluation for many fragments. Another common database model graph databases also requires a heavy use of navigation in queries; yet it largely adopts a different approach to querying, relying on reachability patterns expressed with regular constraints. Our goal here is to investigate the behavior and applicability of XPathlike languages for querying graph databases, concentrating on their expressiveness and complexity of query evaluation. We are particularly interested in a model of graph data that combines navigation through graphs with querying data held in the nodes, such as, for example, in a social network scenario. As navigational languages, we use analogs of core and regular XPath and augment them with various tests on data values. We relate these languages to firstorder logic, its transitive closure extensions, and finitevariable fragments thereof, proving several capture results. In addition, we describe their relative expressive power. We then show that they behave very well computationally: they have a lowdegree polynomial combined complexity, which becomes linear for several fragments. Furthermore, we introduce new types of tests for XPath languages that let them capture firstorder logic with data comparisons and prove that the low complexity bounds continue to apply to such extended languages. Therefore, XPathlike languages seem to be very wellsuited to query graphs.
Synchronizing Relations on Words
"... While the theory of languages of words is very mature, our understanding of relations on words is still lagging behind. And yet such relations appear in many new applications such as verification of parameterized systems, querying graphstructured data, and information extraction, for instance. Clas ..."
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While the theory of languages of words is very mature, our understanding of relations on words is still lagging behind. And yet such relations appear in many new applications such as verification of parameterized systems, querying graphstructured data, and information extraction, for instance. Classes of wellbehaved relations typically used in such applications are obtained by adapting some of the equivalent definitions of regularity of words for relations, leading to nonequivalent notions of recognizable, regular, and rational relations. The goal of this paper is to propose a systematic way of defining classes of relations on words, of which these three classes are just natural examples, and to demonstrate its advantages compared to some of the standard techniques for studying word relations. The key idea is that of a synchronization of a pair of words, which is a word over an extended alphabet. Using it, we define classes of relations via classes of regular languages over a fixed alphabet, just {1, 2} for binary relations. We characterize some of the standard classes of relations on words via finiteness of parameters of synchronization languages, called shift, lag, and shiftlag. We describe these conditions in terms of the structure of cycles of graphs underlying automata, thereby showing their decidability. We show that for these classes there exist canonical synchronization languages, and every class of relations can be effectively resynchronized using those canonical representatives. We also give sufficient conditions on synchronization languages, defined in terms of injectivity and surjectivity of their Parikh images, that guarantee closure under intersection and complement of the classes of relations they define.