Logic for Programming and Automated Reasoning
Volume 1705 of the series Lecture Notes in Computer Science pp 201222
On the Complexity of SingleRule Datalog Queries
 Georg GottlobAffiliated withComputer Science Division, Dept of Electrical Engineering and Computer Science, University of California, Berkeley
 , Christos PapadimitriouAffiliated withComputer Science Division, Dept of Electrical Engineering and Computer Science, University of California, Berkeley
Abstract
Datalog is a wellknown database query language based on the logic programming paradigm. A general datalog program consists of a number of rules and facts. Programs containing a unique rule and possibly some facts are called single rule programs (sirups). We study both the combined and the program complexity of sirups, ie., the complexity of evaluating sirups over variable and fixed databases, respectively. Moreover, we study the descriptive complexity of sirups, i.e., their expressive power. In all cases it turns out that even very restricted classes of sirups have the same complexity and essentially the same expressive power as general datalog programs. We show that the evaluation of single clause programs is EXPTIME complete (combined complexity), and, if restricted to linear recursive rules, PSPACE complete. Moreover, sirups with one recursive rule and one additional fact capture PTIME on ordered structures, if a certain data representation is assumed and certain predefined relations are provided. Our results are obtained by a uniform product construction which maps a datalog program into a single rule by essentially maintaining its semantics. We also prove that the datalog clause implication problem, i.e., deciding whether a datalog clause implies another one, is EXPTIME complete.
 Title
 On the Complexity of SingleRule Datalog Queries
 Book Title
 Logic for Programming and Automated Reasoning
 Book Subtitle
 6th International Conference, LPAR’99 Tbilisi, Georgia, September 6–10, 1999 Proceedings
 Pages
 pp 201222
 Copyright
 1999
 DOI
 10.1007/3540482423_13
 Print ISBN
 9783540664925
 Online ISBN
 9783540482420
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1705
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Harald Ganzinger ^{(1)}
 David McAllester ^{(2)}
 Andrei Voronkov ^{(3)}
 Editor Affiliations

 1. MaxPlanckInstitut für Informatik
 2. AT&T Labs Research
 3. Department of Computer Science, University of Manchester
 Authors

 Georg Gottlob ^{(6)}
 Christos Papadimitriou ^{(6)}
 Author Affiliations

 6. Computer Science Division, Dept of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, 94720
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