### Strong isomorphism reductions in complexity theory

Sam Buss, Yijia Chen, Jörg Flum, Sy-David Friedman, and Moritz Müller
Source: J. Symbolic Logic Volume 76, Issue 4 (2011), 1381-1402.

#### 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.

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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1318338855
Digital Object Identifier: doi:10.2178/jsl/1318338855
Zentralblatt MATH identifier: 05991464
Mathematical Reviews number (MathSciNet): MR2895401

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