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Inf-datalog, Modal Logic and Complexities

Published online by Cambridge University Press:  20 December 2007

Eugénie Foustoucos  and
Irène Guessarian
Eugénie Foustoucos
Affiliation:
MPLA, National and Capodistrian University of Athens, Department of Mathematics, Panepistimiopolis, 15784 Athens, Greece; aflaw@otenet.gr
Irène Guessarian
Affiliation:
LIAFA, UMR 7089, Université Paris 7, case 7014, 2 Place Jussieu, 75251 Paris Cedex 5, France; ig@liafa.jussieu.fr
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Abstract

Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized theexpressive power of various fragments of inf-Datalog in [CITE].In the present paper, we study the complexity of query evaluation on finite modelsfor (various fragments of) inf-Datalog.We deduce a unified and elementary proof that global model-checking (i.e. computing all nodes satisfying a formula in a given structure) has1. quadratic data complexity in timeand linear program complexity in spacefor CTL and alternation-free modal μ-calculus, and2. linear-space (data and program) complexities, linear-time program complexityand polynomial-time data complexity for Lµk (modal μ-calculus with fixed alternation-depth at most k).

Keywords

Databasesmodel-checkingspecification languagesperformance evaluation.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 1 , January 2009 , pp. 1 - 21
Copyright
© EDP Sciences, 2008

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