License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2017.9
URN: urn:nbn:de:0030-drops-85715
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8571/
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Bottesch, Ralph

Relativization and Interactive Proof Systems in Parameterized Complexity Theory

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LIPIcs-IPEC-2017-9.pdf (0.5 MB)

Abstract

We introduce some classical complexity-theoretic techniques to Parameterized Complexity. First, we study relativization for the machine models that were used by Chen, Flum, and Grohe (2005) to characterize a number of parameterized complexity classes. Here we obtain a new and non-trivial characterization of the A-Hierarchy in terms of oracle machines, and parameterize a famous result of Baker, Gill, and Solovay (1975), by proving that, relative to specific oracles, FPT and A[1] can either coincide or differ (a similar statement holds for FPT and W[P]). Second, we initiate the study of interactive proof systems in the parameterized setting, and show that every problem in the class AW[SAT] has a proof system with "short" interactions, in the sense that the number of rounds is upper-bounded in terms of the parameter value alone.

BibTeX - Entry

@InProceedings{bottesch:LIPIcs:2018:8571,
  author =	{Ralph Bottesch},
  title =	{{Relativization and Interactive Proof Systems in Parameterized Complexity Theory}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{9:1--9:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-051-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{89},
  editor =	{Daniel Lokshtanov and Naomi Nishimura},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8571},
  URN =		{urn:nbn:de:0030-drops-85715},
  doi =		{10.4230/LIPIcs.IPEC.2017.9},
  annote =	{Keywords: Parameterized complexity, Relativization, Interactive Proof Systems}
}

Keywords: Parameterized complexity, Relativization, Interactive Proof Systems
Collection: 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)
Issue Date: 2018
Date of publication: 02.03.2018

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