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doi:10.1016/j.entcs.2008.03.011 
Copyright © 2008 Elsevier B.V. All rights reserved.
Complexity of Operators on Compact Sets
Xishun Zhao1, 4, a, 
and Norbert Müller1, 5, b,
aInstitute of Logic and Cognition, Sun Yat-Sen University, 510275 Guangzhou, P.R. China bFB IV, Abteilung Informatik, Universität Trier, D-54286 Trier, Germany
Available online 20 March 2008.
Abstract
Based on oracle Turing machines, we investigate the computational complexity of operators on compact sets. For the projection and convex hull we are able to show exponential upper and lower bounds as well as a connection to the P=NP problem for special settings.
Keywords: Oracle Turing machines; compact sets; operator complexity; projection; convex hull
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1 The authors would like to thank Professor Klaus Weihrauch for his useful comments and suggestions to write this paper, and the anonymous referees for many valuable hints and corrections.
4 Research was partially supported by the NSFC projects under Grant No. 60573011, 10410638 and a MOE project under grant number 05JJD72040122
5 Research was partially supported by the DFG project 446 CHV 113/240/0-1
