On nondeterminism in combinatorial filters

Yulin Zhang, Dylan A. Shell

Abstract: 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 polyno-mial), 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.