On nondeterminism in combinatorial filters

The problem of combinatorial filter reduction arises from resource optimization in robots; it is one specific way in which automation can help to achieve minimalism, to build better 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 may re-use states to obtain 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 complexity result established in this paper: producing nondeterministic minimizers is PSPACE-hard. The hardness separation for minimization existing between deterministic filter and automata, thus, fails to hold for the nondeterministic case.