  Eroders are monotonic cellular automata with a linearly ordered state set
that eventually wipe out any finite island of nonzero states. One-dimensional
eroders were studied by Gal'perin in the 1970s, who presented a simple
combinatorial characterization of the class. The multi-dimensional case has
been studied by Toom and others, but no such characterization has been found.
We prove a similar characterization for those one-dimensional monotonic
cellular automata that are eroders even in the presence of random noise.
