Notre Dame Journal of Formal Logic

On Polynomial-Time Relation Reducibility

Abstract

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 $\mathsf{E}_{\lambda}$ and $\mathsf{id}$. In addition, we consider equivalence relations with finitely many nontrivial equivalence classes and those whose equivalence classes are all finite.

Article information

Source
Notre Dame J. Formal Logic, Volume 58, Number 2 (2017), 271-285.

Dates
Accepted: 29 September 2014
First available in Project Euclid: 3 March 2017

https://projecteuclid.org/euclid.ndjfl/1488510091

Digital Object Identifier
doi:10.1215/00294527-3867118

Mathematical Reviews number (MathSciNet)
MR3634981

Zentralblatt MATH identifier
06751303

Citation

Gao, Su; Ziegler, Caleb. On Polynomial-Time Relation Reducibility. Notre Dame J. Formal Logic 58 (2017), no. 2, 271--285. doi:10.1215/00294527-3867118. https://projecteuclid.org/euclid.ndjfl/1488510091

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