This paper pursues a computational theory that distinguishes between possible and impossible autosegmental tone mapping patterns, in which unassociated tones are mapped to tone-bearing units (TBUs). It shows that tone mapping patterns are describable by a restricted least fixed point logic. This gives a typological characterization of tone association that is unavailable to derivation-based frameworks but can capture patterns that cannot be captured by the alignment constraints used in optimization-based frameworks. Additionally, it resolves earlier issues about the complexity of autosegmental mappings from tones to TBUs noted in the literature. Finally, it provides the first computational definition of output-based locality in functions for non-linear structures.