• Documents
  • Authors
  • Tables
  • Log in
  • Sign up
  • MetaCart
  • DMCA
  • Donate

CiteSeerX logo

Advanced Search Include Citations
Advanced Search Include Citations

Graph logics with rational relations and the generalized intersection problem. (2012)

by P Barceló, D Figueira, L Libkin
Venue:In LICS
Add To MetaCart

Tools

Sorted by:
Results 1 - 10 of 10

Querying graph databases with XPath

by Leonid Libkin, Wim Martens, Domagoj Vrgoč , 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., first-order logic), and the low complexity of query evaluation for many fragments ..."
Abstract - Cited by 16 (3 self) - Add to MetaCart
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., first-order 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 XPath-like 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 first-order 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 low-degree polynomial combined complexity, which becomes linear for several fragments. Furthermore, we introduce new types of tests for XPath languages that let them capture first-order logic with data comparisons and prove that the low complexity bounds continue to apply to such extended languages. Therefore, XPath-like languages seem to be very well-suited to query graphs.
(Show Context)

Citation Context

...nguage over the labeling alphabet [19]. Extensions of RPQs with more complex patterns, backward navigation, relations over paths, and mixing labels and data in nodes have been studied extensively too =-=[1, 6, 7, 11, 12, 18, 32]-=-. Over the past decade, navigational queries have been studied in depth in a different framework extending the relational model, namely in XML. Most formalisms for describing and querying XML cruciall...

COMPLEXITY HIERARCHIES BEYOND ELEMENTARY

by Sylvain Schmitz , 2013
"... We introduce a hierarchy of fast-growing 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 non-elementary complexity, which occur naturally in logic, combinatorics, formal ..."
Abstract - Cited by 11 (4 self) - Add to MetaCart
We introduce a hierarchy of fast-growing 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 non-elementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond.
(Show Context)

Citation Context

...ples of complete problems, this hierarchy includes non primitiverecursive classes, for which quite a few complete problems have arisen in the recent years, e.g. Fω in [58, 43, 83, 75, 29, 14], Fωω in =-=[18, 66, 51, 8, 16, 9]-=-, Fωωω in [40], and Fε0 in [38]. The classes Fα are related to the Grzegorczyk (E k)k [37] and extended Grzegorczyk (Fα)α [56] hierarchies, which have been used in complexity statements for non-elemen...

TriAL for RDF: Adapting Graph Query Languages for RDF Data

by Leonid Libkin, Juan Reutter, Domagoj Vrgoč
"... 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 triples-based model of RDF. While encodings of RDF databases into graph data exist, we show that even the most natu ..."
Abstract - Cited by 8 (3 self) - Add to MetaCart
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 triples-based 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 low-degree polynomials. We compare our languages with relational languages, such as finite-variable 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.
(Show Context)

Citation Context

... in TriAL ∗ . There are further extensions, such as extended CRPQs, where paths witnessing RPQs can be named and compared for relationships between them, defined as regular or even rational relations =-=[6, 7]-=-. We leave the comparison with these languages as future work. 6.2.2 Query languages for graphs with data Until now we have compared our algebra with purely navigationalformalisms. Triple stores do ha...

GRAPH LOGICS WITH RATIONAL RELATIONS

by Pablo Barceló, Diego Figueira, Leonid Libkin
"... 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 ..."
Abstract - Cited by 5 (2 self) - Add to MetaCart
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 non-primitive-recursive 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 non-primitive-recursive 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.
(Show Context)

Citation Context

...words and phrases: Regular relations; Rational relations; Recognizable relations; intersection problem; RPQ; graph databases; non primitive recursive. This is the full version of the conference paper =-=[3]-=-. Partial support provided by Fondecyt grant 1110171, EPSRC grant G049165, and FET-Open Project FoX, grant agreement 233599. LOGICAL METHODS IN COMPUTER SCIENCE DOI:10.2168/LMCS-??? c○ P. Barceló, D. ...

Spanners: A Formal Framework for Information Extraction

by Ronald Fagin, Benny Kimelfeld, Frederick Reiss, Stijn Vansummeren , 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 ..."
Abstract - Cited by 5 (4 self) - Add to MetaCart
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 string-equality 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.
(Show Context)

Citation Context

...iables (of the same arity as R) is in R. We say that R is selectable by a class of spanners (e.g., the regular or core) if that class is closed under the selection operator for R. Like Barceló et al. =-=[5]-=-, we look at three classes of string relations: the recognizable relations [8,20], which are contained in the regular relations [7,20], which are contained in the rational relations [8, 39]. We show t...

The Power of Well-Structured Systems

by S. Schmitz, Ph. Schnoebelen
"... Well-structured systems, aka WSTS, are computational models where the set of possible configurations is equipped with a well-quasiordering which is compatible with the transition relation between configurations. This structure supports generic decidability results that are important in verificatio ..."
Abstract - Cited by 5 (0 self) - Add to MetaCart
Well-structured systems, aka WSTS, are computational models where the set of possible configurations is equipped with a well-quasiordering 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 well-structured 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 complexity-theoretical sense, of several important WSTS models like unreliable channel systems, monotonic counter machines, or networks of timed systems.
(Show Context)

Citation Context

...ent papers rely on reductions to (or from) a known WSTS problem to show the decidability (or the hardness) of problems in unrelated fields, from modal and temporal logic [31, 38] to XPathlike queries =-=[29, 7]-=-. Outline of the paper. Section 1 recalls the definition of WSTS, Sec.2 illustrates it with a simple example, while Sec.3 presents the two main verification algorithms for WSTS. Section 4 bounds the r...

The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

by Prateek Karandikar, Sylvain Schmitz , 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 multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) an ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
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 multiply-recursive 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 Context-Free Path Queries

by Jelle Hellings , 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 context-free grammars. With the Conjunctive Context-Free Path Queries (CCFPQ) we introduce ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
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 context-free grammars. With the Conjunctive Context-Free Path Queries (CCFPQ) we introduce such a language based on the well-known 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 context-free 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 context-free grammars does increase expressive power. Finally, we look at including context-free grammars in more powerful log-ics than conjunctive queries. We do so by adding negation and provide expressivity relations between the obtained languages.
(Show Context)

Citation Context

...Context-free grammars over tuples CCFPQ, as does CRPQ, lack mechanisms to compare paths. In the case of CRPQ, path comparisons have been added by generalizing regular expressions to regular relations =-=[4, 5, 13]-=-. Usually, these regular relations are specified by regular expressions over tuples of edge labels and are used in combination with path variables resulting in the Extended Conjunctive Regular Path Qu...

Querying Graph Databases with XPath General Terms

by Leonid Libkin , Wim Martens , Domagoj Vrgoč
"... 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., first-order logic), and the low complexity of query evaluation for many fragments. An ..."
Abstract - Add to MetaCart
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., first-order 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 XPath-like 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 first-order 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 low-degree polynomial combined complexity, which becomes linear for several fragments. Furthermore, we introduce new types of tests for XPath languages that let them capture first-order logic with data comparisons and prove that the low complexity bounds continue to apply to such extended languages. Therefore, XPath-like languages seem to be very well-suited to query graphs.
(Show Context)

Citation Context

...e, about information on people in a social network. What makes graph databases different, however, is the ability to ask queries about their topology, essentially looking for reachability patterns and, more generally, subgraph patterns [11, 21, 20]. A basic building block for such queries is typically a regular path query, or an RPQ, that selects nodes connected by a path described by a regular language over the labeling alphabet [19]. Extensions of RPQs with more complex patterns, backward navigation, relations over paths, and mixing labels and data in nodes have been studied extensively too [1, 6, 7, 11, 12, 18, 32]. Over the past decade, navigational queries have been studied in depth in a different framework extending the relational model, namely in XML. Most formalisms for describing and querying XML crucially depend on its path language XPath [44]. The goal of XPath is seemingly very similar to the goal of many queries in graph databases: it describes properties of paths, taking into account both their purely navigational properties and data that is found in XML documents. The popularity of XPath is largely due to several factors: • it defines many properties of paths that are relevant for navigation...

Synchronizing Relations on Words

by Diego Figueira, Leonid Libkin
"... 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 graph-structured data, and information extraction, for instance. Clas ..."
Abstract - Add to MetaCart
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 graph-structured data, and information extraction, for instance. Classes of well-behaved relations typically used in such applications are obtained by adapting some of the equivalent definitions of regularity of words for relations, leading to non-equivalent 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 re-synchronized 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.
Powered by: Apache Solr
  • About CiteSeerX
  • Submit and Index Documents
  • Privacy Policy
  • Help
  • Data
  • Source
  • Contact Us

Developed at and hosted by The College of Information Sciences and Technology

© 2007-2019 The Pennsylvania State University