  A symbolic analysis of observed time series data requires making a discrete
partition of a continuous state space containing observations of the dynamics.
A particular kind of partition, called ``generating'', preserves all dynamical
information of a deterministic map in the symbolic representation, but such
partitions are not obvious beyond one dimension, and existing methods to find
them require significant knowledge of the dynamical evolution operator or the
spectrum of unstable periodic orbits. We introduce a statistic and algorithm to
refine empirical partitions for symbolic state reconstruction. This method
optimizes an essential property of a generating partition: avoiding topological
degeneracies. It requires only the observed time series and is sensible even in
the presence of noise when no truly generating partition is possible. Because
of its resemblance to a geometrical statistic frequently used for
reconstructing valid time-delay embeddings, we call the algorithm ``symbolic
false nearest neighbors''.
