We study the notion of polynomial-time relation reducibility among computable equivalence relations. We identify some benchmark equivalence relations and show that the reducibility hierarchy has a rich structure. Specifically, we embed the partial order of all polynomial-time computable sets into the polynomial-time relation reducibility hierarchy between two benchmark equivalence relations and . In addition, we consider equivalence relations with finitely many nontrivial equivalence classes and those whose equivalence classes are all finite.
"On Polynomial-Time Relation Reducibility." Notre Dame J. Formal Logic 58 (2) 271 - 285, 2017. https://doi.org/10.1215/00294527-3867118