  The problem of combinatorial filter reduction arises from questions of
resource optimization in robots; it is one specific way in which automation can
help to achieve minimalism, to build better, simpler robots. This paper
contributes a new definition of filter minimization that is broader than its
antecedents, allowing filters (input, output, or both) to be nondeterministic.
This changes the problem considerably. Nondeterministic filters are able to
re-use states to obtain, essentially, more 'behavior' per vertex. We show that
the gap in size can be significant (larger than polynomial), suggesting such
cases will generally be more challenging than deterministic problems. Indeed,
this is supported by the core computational complexity result established in
this paper: producing nondeterministic minimizers is PSPACE-hard. The hardness
separation for minimization which exists between deterministic filter and
deterministic automata, thus, does not hold for the nondeterministic case.
