Pebble games with algebraic rules
Abstract
We define a general framework of partition games for formulating two-player pebble games over finite structures. We show that one particular such game, 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-Lehman method. The general 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 matrix-rank logic. We show that the equivalence defined by the invertible-map game is a refinement of the equivalence defined by each of these games for finite-variable logics.
Cite
@article{arxiv.1205.0913,
title = {Pebble games with algebraic rules},
author = {Anuj Dawar and Bjarki Holm},
journal= {arXiv preprint arXiv:1205.0913},
year = {2015}
}