Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 58, Number 2 (2017), 271-285.
On Polynomial-Time Relation Reducibility
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.
Notre Dame J. Formal Logic, Volume 58, Number 2 (2017), 271-285.
Received: 10 February 2014
Accepted: 29 September 2014
First available in Project Euclid: 3 March 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03D15: Complexity of computation (including implicit computational complexity) [See also 68Q15, 68Q17] 68Q15: Complexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68Q19]
Secondary: 68Q17: Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also 68Q15]
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