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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/16521

Title: Regular graphs and the spectra of two-variable logic with counting
Authors: TAN, Tony
Issue Date: 2013
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 spectra of first-order logic sentences are semilinear 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.
URI: http://hdl.handle.net/1942/16521
Link to publication: http://arxiv.org/abs/1304.0829
Category: O
Type: Preprint
Appears in Collections: Research publications

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