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Issue RAIRO-Theor. Inf. Appl.
Volume 42, Number 1, January-March 2008
A nonstandard spirit among computer scientists:
a tribute to Serge Grigorieff at the occasion of his 60th birthday
Page(s) 121 - 135
DOI 10.1051/ita:2007047
Published online 18 January 2008

RAIRO-Theor. Inf. Appl. 42, 121-135 (2008)
DOI: 10.1051/ita:2007047

Deciding whether a relation defined in Presburger logic can be defined in weaker logics

Christian Choffrut

LIAFA, Université de Paris 7, 2 place Jussieu, 75251 Paris Cedex 05; cc@liafa.jussieu.fr


(Published online: 18 January 2008)

Abstract
We consider logics on $\mathbb{Z} $ and $\mathbb{N} $ which are weaker than Presburger arithmetic and we settle the following decision problem: given a k-ary relation on $\mathbb{Z} $ and $\mathbb{N} $ which are first order definable in Presburger arithmetic, are they definable in these weaker logics? These logics, intuitively, are obtained by considering modulo and threshold counting predicates for differences of two variables.


Mathematics Subject Classification. 03B10, 68Q70

Key words: Presburger arithmetic -- first order logic -- decidability


© EDP Sciences 2007


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