Journal of Symbolic Logic

Strong isomorphism reductions in complexity theory

Sam Buss, Yijia Chen, Jörg Flum, Sy-David Friedman, and Moritz Müller

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Abstract

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 4 (2011), 1381-1402.

Dates
First available in Project Euclid: 11 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1318338855

Digital Object Identifier
doi:10.2178/jsl/1318338855

Mathematical Reviews number (MathSciNet)
MR2895401

Zentralblatt MATH identifier
1248.03060

Citation

Buss, Sam; Chen, Yijia; Flum, Jörg; Friedman, Sy-David; Müller, Moritz. Strong isomorphism reductions in complexity theory. J. Symbolic Logic 76 (2011), no. 4, 1381--1402. doi:10.2178/jsl/1318338855. https://projecteuclid.org/euclid.jsl/1318338855


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