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Date:
08 Jun 2005
Query languages with counters
 Stéphane Grumbach,
 Christophe Tollu
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Abstract
We investigate the expressive power of query languages with counting ability. We define a LOGSPACE extension of first order logic and a PTIME extension of fixpoint logic with counters. We develop specific techniques, such as games, for dealing with languages with counters and therefore integers. We prove in particular that the arity of the tuples which are counted induces a strict expressivity hierarchy. We also establish results about the asymptotic probabilities of sentences with counters. In particular we show that first order logic with comparison of the cardinalities of relations has a. 0/1 law.
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 Title
 Query languages with counters
 Book Title
 Database Theory — ICDT '92
 Book Subtitle
 4th International Conference Berlin, Germany, October 14–16, 1992 Proceedings
 Pages
 pp 124139
 Copyright
 1992
 DOI
 10.1007/3540560394_37
 Print ISBN
 9783540560395
 Online ISBN
 9783540473602
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 646
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Stéphane Grumbach ^{(1)}
 Christophe Tollu ^{(2)}
 Author Affiliations

 1. I.N.R.I.A., Rocquencourt, BP 105, 78153, Le Chesnay, France
 2. LIPNInstitut Galilée, Université ParisNord, 93430, Villetaneuse, France
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