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Journal of Logic and Computation 2005 15(5):577-592; doi:10.1093/logcom/exi022
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Vol. 15 No. 5, © The Author, 2005. Published by Oxford University Press. All rights reserved.

Original Articles

P != NP {cap} co-NP for Infinite Time Turing Machines

Vinay Deolalikar1, Joel David Hamkins2 and Ralf Schindler3

1 Hewlett-Packard Research, 1501 Page Mill Road, M/S 3U-4, Palo Alto, CA 94304, USA. Email: vinay.deolalikar{at}hp.com, 2 The College of Staten Island of CUNY & The CUNY Graduate Center, Mathematics Program, 365 Fifth Avenue, New York, NY 10016, USA. Email: jdh{at}hamkins.org, 3 Institut für mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany. Email: rds{at}math.uni-muenster.de

Extending results of Schindler, Hamkins and Welch, we establish in the context of infinite time Turing machines that P is properly contained in NP {cap} co-NP. For higher analogues of these classes, we exhibit positive and negative results.

Keywords: Infinite time Turing machines, complexity theory, descriptive set theory

Received 24 November 2003.


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