Chapter

Database Theory — ICDT '92

Volume 646 of the series Lecture Notes in Computer Science pp 124-139

Date:

Query languages with counters

  • Stéphane GrumbachAffiliated withI.N.R.I.A.
  • , Christophe TolluAffiliated withLIPN-Institut Galilée, Université Paris-Nord

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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.