Notre Dame Journal of Formal Logic

On Polynomial-Time Relation Reducibility

Su Gao and Caleb Ziegler

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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 Eλ and id. In addition, we consider equivalence relations with finitely many nontrivial equivalence classes and those whose equivalence classes are all finite.

Article information

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

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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]

polynomial-time relation reducibility strong reduction function finitary equivalence relations finite equivalence relations


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.

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