Sparse Sets, Tally Sets, and Polynomial Reducibilities

The properties of resource-bounded reducibilities have received a great deal of attention in the study of structural complexity theory. Recently, the properties of the corresponding reduction classes and degrees of sparse sets and of tally sets have been investigated. In some cases this has been done in the context of properties of reducibilities, which in other cases the motivation was quite different. There are some important examples of results about sparse sets and tally sets, and these include the following:

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