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International Conference on Current Trends in Theory and Practice of Computer Science

SOFSEM 2006: SOFSEM 2006: Theory and Practice of Computer Science pp 323–331Cite as

P-Selectivity, Immunity, and the Power of One Bit

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3831))

Abstract

We prove that P-sel, the class of all P-selective sets, is EXP-immune, but is not EXP/1-immune. That is, we prove that some infinite P-selective set has no infinite EXP-time subset, but we also prove that every infinite P-selective set has some infinite subset in EXP/1. Informally put, the immunity of P-sel is so fragile that it is pierced by a single bit of information.

The above claims follow from broader results that we obtain about the immunity of the P-selective sets. In particular, we prove that for every recursive function f, P-sel is DTIME(f)-immune. Yet we also prove that P-sel is not \({\it \Pi}^{p}_{2}\)/1-immune.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Rochester, Rochester, NY, 14627, USA

    Lane A. Hemaspaandra

  2. ILLC, University of Amsterdam, 1018 TV 24, Amsterdam, The Netherlands

    Leen Torenvliet

Authors
  1. Lane A. Hemaspaandra
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  2. Leen Torenvliet
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Jiří Wiedermann  & Július Štuller  & 

  2. Department of Information and Computer Sciences, University of Utrecht, P.O. Box 80.089, 3508, Utrecht, TB, The Netherlands

    Gerard Tel

  3. Faculty of Mathematics and Physics, Charles University, Prague

    Jaroslav Pokorný

  4. Institute of Informatics and Software Engineering Faculty of Informatics and Information technologies, Slovak University of Technology, Ilkovičova 3, 842 16, Bratislava

    Mária Bieliková

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© 2006 Springer-Verlag Berlin Heidelberg

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Hemaspaandra, L.A., Torenvliet, L. (2006). P-Selectivity, Immunity, and the Power of One Bit. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_30

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  • DOI: https://doi.org/10.1007/11611257_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31198-0

  • Online ISBN: 978-3-540-32217-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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