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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/18320

Title: Regular graphs and the spectra of two-variable logic with counting
Authors: Tan, Tony
Kopczynski, Eryk
Issue Date: 2015
Citation: SIAM JOURNAL ON COMPUTING, 44(3), p. 786-818
Abstract: The spectrum of a first-order logic sentence is the set of natural numbers that are cardinalities of its finite models.In this paper we show that when restricted to using only two variables, but allowing counting quantifiers, the class of spectra of first-order logic sentences is exactly the class of semilinear sets, and hence, closed under complement. At the heart of our proof are semilinear characterisations for the existence of regular and biregular graphs, the class of graphs in which there are a priori bounds on the degrees of the vertices. Our proof also provides a simple characterisation of models of two-variable logic with counting -- that is, up to renaming and extending the relation names, they are simply a collection of regular and biregular graphs.
Notes: [Kopczynski, Eryk] Univ Warsaw, PL-02097 Warsaw, Poland. [Tan, Tony] Hasselt Univ, BE-3590 Diepenbeek, Belgium. [Tan, Tony] Transnat Univ Limburg, Fac Sci, BE-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/18320
DOI: 10.1137/130943625
ISI #: 000357414100007
ISSN: 0097-5397
Category: A1
Type: Journal Contribution
Validation: ecoom, 2016
Appears in Collections: Research publications

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