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Expressive Power and Data Complexity of Query Languages for Trees and Lists
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Evgeny Dantsin and
Andrei Voronkov
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Abstract
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We extend the traditional query languages by primitives for handling lists and trees. Our main results characterize the expressive power and data complexity of the following extended languages: (1) relational algebra with lists and trees, (2) nonrecursive Datalog with lists and trees, (3) nonrecursive Prolog with lists and trees, (4) first-order logic over lists and trees.
Languages (2)-(4) turn out to have the same expressive power; their range-restricted fragments have the same expressive power as (1). Every query in these languages is a boolean combination of range-restricted queries.
We also prove that these query languages have polynomial data complexity under any "reasonable" encoding of inputs. Furthermore, under a natural encoding of inputs, languages (2)-(4) have the same expressive power as first-order logic over finite structures, therefore their data complexity is in A Co. Thus, the use of lists and trees in nonrecursive query languages gives no gain in the expressiveness. This contrasts with a huge difference between the nonelementary program complexity of extended languages (2)-(4) and the PSPACE program complexity of their relational counterparts.
Our results partly explain why lists and trees are not so widely used in nonrecursive query languages as other collection types.
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References
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Note: References link to DBLP on the Web.
-
[1]
-
Serge Abiteboul
,
Richard Hull
,
Victor Vianu
: Foundations of Databases. Addison-Wesley 1995, ISBN 0-201-53771-0
Contents
-
[2]
-
Serge Abiteboul
,
Victor Vianu
: Datalog Extensions for Database Queries and Updates.
JCSS 43(1)
: 62-124(1991)
-
[3]
-
Alfred V. Aho
,
Jeffrey D. Ullman
: The Universality of Data Retrieval Languages.
POPL 1979
: 110-120
-
[4]
-
Krzysztof R. Apt
: Logic Programming.
Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics (B) 1990
: 493-574
-
[5]
-
Michael Benedikt
,
Leonid Libkin
: Languages for Relational Databases over Interpreted Structures.
PODS 1997
: 87-98
-
[6]
-
Michael Benedikt
,
Leonid Libkin
: Safe Constraint Queries.
PODS 1998
: 99-108
-
[7]
-
Leonard Berman
: The Complexitiy of Logical Theories.
TCS 11
: 71-77(1980)
-
[8]
-
Howard A. Blair
,
V. Wiktor Marek
,
John S. Schlipf
: The Expressiveness of Locally Stratified Programs.
Annals of Mathematics and Artificial Intelligence 15(2)
: 209-229(1995)
-
[9]
-
Ashok K. Chandra
,
David Harel
: Structure and Complexity of Relational Queries.
JCSS 25(1)
: 99-128(1982)
-
[10]
-
Latha S. Colby
,
Edward L. Robertson
,
Lawrence V. Saxton
,
Dirk Van Gucht
: A Query Language for List-Based Complex Objects.
PODS 1994
: 179-189
-
[11]
-
Kevin J. Compton
,
C. Ward Henson
: A Uniform Method for Proving Lower Bounds on the Computational Complexity of Logical Theories.
Annals of Pure and Applied Logic 48(1)
: 1-79(1990)
-
[12]
-
Evgeny Dantsin
,
Thomas Eiter
,
Georg Gottlob
,
Andrei Voronkov
: Complexity and Expressive Power of Logic Programming.
IEEE Conference on Computational Complexity 1997
: 82-101
-
[13]
-
...
-
[14]
-
...
-
[15]
-
...
-
[16]
-
...
-
[17]
-
Richard Hull
,
Jianwen Su
: Algebraic and Calculus Query Languages for Recursively Typed Complex Objects.
JCSS 47(1)
: 121-156(1993)
-
[18]
-
Richard Hull
,
Jianwen Su
: Domain Independence and the Relational Calculus.
Acta Informatica 31(6)
: 513-524(1994)
-
[19]
-
Neil Immerman
: Relational Queries Computable in Polynomial Time.
Information and Control 68(1-3)
: 86-104(1986)
-
[20]
-
Neil Immerman
: Languages that Capture Complexity Classes.
SIAM J. Comput. 16(4)
: 760-778(1987)
-
[21]
-
Paris C. Kanellakis
,
Gabriel M. Kuper
,
Peter Z. Revesz
: Constraint Query Languages.
JCSS 51(1)
: 26-52(1995)
-
[22]
-
Gabriel M. Kuper
,
Moshe Y. Vardi
: The Logical Data Model.
TODS 18(3)
: 379-413(1993)
-
[23]
-
Gabriel M. Kuper
,
Moshe Y. Vardi
: On the Complexity of Queries in the Logical Data Model.
TCS 116(1&2)
: 33-57(1993)
-
[24]
-
Michael J. Maher
: Complete Axiomatizations of the Algebras of Finite, Rational and Infinite Trees.
LICS 1988
: 348-357
-
[25]
-
...
-
[26]
-
Jan Paredaens
,
Jan Van den Bussche
,
Dirk Van Gucht
: First-order Queries on Finite Structures over the Reals.
LICS 1995
: 79-87
-
[27]
-
...
-
[28-1]
-
Jeffrey D. Ullman
: Principles of Database and Knowledge-Base Systems, Volume I. Computer Science Press 1988, ISBN 0-7167-8158-1
Contents
-
[28-2]
-
Jeffrey D. Ullman
: Principles of Database and Knowledge-Base Systems, Volume II. Computer Science Press 1989, ISBN 0-7167-8162-X
Contents
-
[29]
-
Luc Vandeurzen
,
Marc Gyssens
,
Dirk Van Gucht
: An Expressive Language for Linear Spatial Database Queries.
PODS 1998
: 109-118
-
[30]
-
Moshe Y. Vardi
: The Complexity of Relational Query Languages (Extended Abstract).
STOC 1982
: 137-146
-
[31]
-
...
-
[32]
-
Hugo Volger
: Turing Machines with Linear Alternation, Theories of Bounded Concatenation and the Decision Problem of First Order Theories.
TCS 23
: 333-337(1983)
-
[33]
-
Sergei G. Vorobyov
: An Improved Lower Bound for the Elementary Theories of Trees.
CADE 1996
: 275-287
-
[34]
-
Sergei G. Vorobyov
,
Andrei Voronkov
: Complexity of Nonrecursive Logic Programs with Complex Values.
PODS 1998
: 244-253
Referenced by
-
Jan Van den Bussche
: Constraint databases: A tutorial introduction.
SIGMOD Record 29(3)
: 44-51(2000)
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BIBTEX
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@inproceedings{DBLP:conf/pods/DantsinV00,
author = {Evgeny Dantsin and
Andrei Voronkov},
title = {Expressive Power and Data Complexity of Query Languages for Trees
and Lists},
booktitle = {Proceedings of the Nineteenth ACM SIGMOD-SIGACT-SIGART Symposium
on Principles of Database Systems, May 15-17, 2000, Dallas, Texas,
USA},
publisher = {ACM},
year = {2000},
isbn = {1-58113-214-X},
pages = {157-165},
crossref = {DBLP:conf/pods/00},
bibsource = {DBLP, http://dblp.uni-trier.de} } },
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