We address the problem of estimating discrete variables in a class of deterministic transition systems in which the continuous variables are available for measurement. We propose a novel approach to the estimation of discrete variables using lattice theory that overcomes some of the severe complexity issues encountered in previous work. The methodology proposed for the estimation of discrete variables is general as it is applicable to any observable system. Extensions generalize the approach to nondeterministic transition systems. The proposed estimator is finally constructed for a multi-robot system involving two teams competing against each other. (c) 2005 Elsevier Ltd. All rights reserved.