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Issue title: Fixed Points in Computer Science (FICS) 2013
Guest editors: David Baelde, Arnaud Carayol, Ralph Matthes and Igor Walukiewicz
Article type: Research Article
Authors: Dawar, Anuja; † | Holm, Bjarkib
Affiliations: [a] Computer Laboratory, University of Cambridge, United Kingdom. [email protected] | [b] Twigkit ltd., United Kingdom. [email protected]
Correspondence: [C] Address for correspondence: Computer Laboratory, University of Cambridge, United Kingdom
Note: [*] Research supported by EPSRC grant EP/H026835/1. An extended abstract of this paper appeared in the proceedings of ICALP 2012.
Abstract: We define a general framework of partition games for formulating two-player pebble games over finite structures. The framework we introduce includes as special cases the pebble games for finite-variable logics with and without counting. It also includes a matrix-equivalence game, introduced here, which characterises equivalence in the finite-variable fragments of the matrix-rank logic of [Dawar et al. 2009]. We show that one particular such game in our framework, which we call the invertible-map game, yields a family of polynomial-time approximations of graph isomorphism that is strictly stronger than the well-known Weisfeiler-Leman method. We show that the equivalence defined by this game is a refinement of the equivalence defined by each of the games for finite-variable logics.
DOI: 10.3233/FI-2017-1471
Journal: Fundamenta Informaticae, vol. 150, no. 3-4, pp. 281-316, 2017
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