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Strong isomorphism reductions in complexity theory

Published online by Cambridge University Press:  12 March 2014

Sam Buss ,
Yijia Chen ,
Jörg Flum ,
Sy-David Friedman  and
Moritz Müller
Sam Buss
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112, USA, E-mail: sbuss@math.ucsd.edu
Yijia Chen
Affiliation:
Basic Studies in Computing Science (Basics), Department of Computer Science, Shanghai Jiaotong University, Shanghai 200030, China, E-mail: yijia.chen@cs.sjtu.edu.cn
Jörg Flum
Affiliation:
Mathematisches Institut, Albert-Ludwigs Universität Freiburg, 79104 Freiburg, Germany, E-mail: joerg.flum@math.uni-freiburg.de
Sy-David Friedman
Affiliation:
Kurt Gödel Research Center, Währinger Straße 25, A-1090 Wien, Austria, E-mail: sdf@logic.univie.ac.at
Moritz Müller
Affiliation:
Centre de Recerca Matemàtica, Campus Bellaterra, Edifici C, 08193 Bellaterra (Barcelona), Spain, E-mail: mmueller@crm.cat
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1381 - 1402
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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