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50
Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 366 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
On the Complexity of Nonrecursive XQuery and Functional Query Languages on Complex Values
 In Proc. PODS’05
"... This article studies the complexity of evaluating functional query languages for complex values such as monad algebra and the recursionfree fragment of XQuery. We show that monad algebra with equality restricted to atomic values is complete for the class TA[2O(n) , O(n)] of problems solvable in lin ..."
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Cited by 47 (2 self)
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This article studies the complexity of evaluating functional query languages for complex values such as monad algebra and the recursionfree fragment of XQuery. We show that monad algebra with equality restricted to atomic values is complete for the class TA[2O(n) , O(n)] of problems solvable in linear exponential time with a linear number of alternations. The monotone fragment of monad algebra with atomic value equality but without negation is complete for nondeterministic exponential time. For monad algebra with deep equality, we establish TA[2O(n) , O(n)] lower and exponentialspace upper bounds. We also study a fragment of XQuery, Core XQuery, that seems to incorporate all the features of a query language on complex values that are traditionally deemed essential. A close connection between monad algebra on lists and Core XQuery (with “child ” as the only axis) is exhibited, and it is shown that these languages are expressively equivalent up to representation issues. We show that Core XQuery is just as hard as monad algebra w.r.t. query and combined complexity, and that it is in TC0 if the query is assumed fixed. As Core XQuery is NEXPTIMEhard, it is commonly believed that any algorithm for evaluating Core XQuery has to require exponential amounts of working memory and doubly exponential time in the worst case. We present a property of queries – the lack of a certain form of composition – that virtually all realworld XQueries have and that allows for query evaluation in singly exponential time and polynomial space. Still, we are able to show for an important special case – Core XQuery with equality testing restricted to atomic values – that the compositionfree language is just as expressive as the language with composition. Thus, under widelyheld complexitytheoretic assumptions, the compositionfree language is an exponentially less succinct version of the language with composition.
Deductive Database Languages: Problems and Solutions
, 1999
"... Deductive databases result from the integration of relational database and logic programming techniques. However, significant problems remain inherent in this simple synthesis from the language point of view. In this paper, we discuss these problems from four different aspects: complex values, objec ..."
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Cited by 25 (4 self)
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Deductive databases result from the integration of relational database and logic programming techniques. However, significant problems remain inherent in this simple synthesis from the language point of view. In this paper, we discuss these problems from four different aspects: complex values, object orientation, higherorderness, and updates. In each case, we examine four typical languages that address the corresponding issues.
Foundations of rulebased query answering
 IN REASONING WEB, INT. SUMMER SCHOOL, LNCS
, 2007
"... This survey article introduces into the essential concepts and methods underlying rulebased query languages. It covers four complementary areas: declarative semantics based on adaptations of mathematical logic, operational semantics, complexity and expressive power, and optimisation of query evalua ..."
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Cited by 19 (10 self)
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This survey article introduces into the essential concepts and methods underlying rulebased query languages. It covers four complementary areas: declarative semantics based on adaptations of mathematical logic, operational semantics, complexity and expressive power, and optimisation of query evaluation. The treatment of these areas is foundationoriented, the foundations having resulted from over four decades of research in the logic programming and database communities on combinations of query languages and rules. These results have later formed the basis for conceiving, improving, and implementing several Web and Semantic Web technologies, in particular query languages such as XQuery or SPARQL for querying relational, XML, and RDF data, and rule languages like the “Rule Interchange Framework (RIF) ” currently being developed in a working group of the W3C. Coverage of the article is deliberately limited to declarative languages in a classical setting: issues such as query answering in FLogic or in description logics, or the relationship of query answering to reactive rules and events, are not addressed.
Complexity of Nonrecursive Logic Programs with Complex Values
 In Proceedings of the 17th ACM SIGACTSIGMODSIGART Symposium on Principles of Database Systems (PODS’98
, 1998
"... We investigate complexity of the SUCCESS problem for logic query languages with complex values: check whether a query defines a nonempty set. The SUCCESS problem for recursive query languages with complex values is undecidable, so we study the complexity of nonrecursive queries. By complex values we ..."
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Cited by 18 (2 self)
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We investigate complexity of the SUCCESS problem for logic query languages with complex values: check whether a query defines a nonempty set. The SUCCESS problem for recursive query languages with complex values is undecidable, so we study the complexity of nonrecursive queries. By complex values we understand values such as trees, finite sets, and multisets. Due to the wellknown correspondence between relational query languages and datalog, our results can be considered as results about relational query languages with complex values. The paper gives a complete complexity classification of the SUCCESS problem for nonrecursive logic programs over trees depending on the underlying signature, presence of negation, and range restrictedness. We also prove several results about finite sets and multisets. 1 Introduction A number of complexity results have been established for logic query languages. They are surveyed in [49, 18]. The major themes in these results are the complexity and expr...
Complexity of Query Answering in Logic Databases with Complex Values
 in S. Adian & A. Nerode, eds, `Logical Foundations of Computer Science. 4th International Symposium, LFCS'97
, 1998
"... This paper characterizes the computational complexity of nonrecursive queries in logic databases with complex values. Queries are represented by Horn clause logic programs. Complex values are represented by terms in equational theories (finite sets and multisets are examples of such complex values). ..."
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Cited by 12 (4 self)
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This paper characterizes the computational complexity of nonrecursive queries in logic databases with complex values. Queries are represented by Horn clause logic programs. Complex values are represented by terms in equational theories (finite sets and multisets are examples of such complex values). We show that the problem of whether a query has a nonempty answer is NEXPhard for nonrecursive rangerestricted queries. We also show that this problem is in NEXP if complex values satisfy the following condition: the solvability problem for equations in the corresponding equational theory is in NP. Since trees, finite sets and multisets satisfy this condition, the query answering problem for logic databases with trees, finite sets and multisets is shown to be NEXPcomplete. 2 2 Copyright c fl 1997, 1998 Evgeni Dantsin and Andrei Voronkov. This technical report and other technical reports in this series can be obtained at http://www.csd.uu.se/papers/reports.html or at ftp.csd.uu.se in th...
A Framework for the Investigation of Aggregate Functions in Database Queries
 IN INTERNATIONAL CONFERENCE ON DATA BASE THEORY 1999, SPRINGER LNCS
, 1999
"... In this paper we present a new approach for studying aggregations in the context of database query languages. Starting from a broad definition of aggregate function, we address our investigation from two different perspectives. We first propose a declarative notion of uniform aggregate function ..."
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Cited by 10 (0 self)
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In this paper we present a new approach for studying aggregations in the context of database query languages. Starting from a broad definition of aggregate function, we address our investigation from two different perspectives. We first propose a declarative notion of uniform aggregate function that refers to a family of scalar functions uniformly constructed over a vocabulary of basic operators by a bounded Turing Machine. This notion yields an effective tool to study the effect of the embedding of a class of builtin aggregate functions in a query language. All the aggregate functions most used in practice are included in this classification. We then present an operational notion of aggregate function, by considering a highorder folding constructor, based on structural recursion, devoted to compute numeric aggregations over complex values. We show that numeric folding over a given vocabulary is sometimes not able to compute, by itself, the whole class of uniform aggre...
A Compositional Query Algebra for SecondOrder Logic and Uncertain Databases
 In Proc. ICDT
, 2009
"... Worldset algebra is a variablefree query language for uncertain databases. It constitutes the core of the query language implemented in MayBMS, an uncertain database system. This paper shows that worldset algebra captures exactly secondorder logic over finite structures, or equivalently, the pol ..."
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Cited by 9 (4 self)
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Worldset algebra is a variablefree query language for uncertain databases. It constitutes the core of the query language implemented in MayBMS, an uncertain database system. This paper shows that worldset algebra captures exactly secondorder logic over finite structures, or equivalently, the polynomial hierarchy. The proofs also imply that worldset algebra is closed under composition, a previously open problem. 1.
Design and Implementation of the Relationlog Deductive Database System
 In Proceedings of the 9th International Workshop on Database and Expert System Applications (DEXA Workshop '98
, 1998
"... We describe the design and implementation of Relationlog, a persistent deductive database system. Unlike other related systems such as Aditi, CORAL, LDL, LOLA and NailGlue, Relationlog supports effective storage, efficient access and inference of large amounts of data with complex structures and pr ..."
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Cited by 8 (7 self)
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We describe the design and implementation of Relationlog, a persistent deductive database system. Unlike other related systems such as Aditi, CORAL, LDL, LOLA and NailGlue, Relationlog supports effective storage, efficient access and inference of large amounts of data with complex structures and provides declarative query language that can define recursive views involving complex data and also a declarative data manipulation language to update databases.
A Safe Relational Calculus for Functional Logic Deductive Databases
, 2003
"... In this paper, we present an extended relational calculus for expressing queries in functionallogic deductive databases. This calculus is based on firstorder logic and handles relation predicates, equalities and inequalities over partially defined terms, and approximation equations. For the calcu ..."
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Cited by 5 (1 self)
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In this paper, we present an extended relational calculus for expressing queries in functionallogic deductive databases. This calculus is based on firstorder logic and handles relation predicates, equalities and inequalities over partially defined terms, and approximation equations. For the calculus formulas, we have studied syntactic conditions in order to ensure the domain independence property. Finally, we have studied its equivalence w.r.t. the original query language, which is based on equality and inequality constraints.