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DOI: 10.4230/LIPIcs.IPEC.2017.9
URN: urn:nbn:de:0030-drops-85715
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8571/
Bottesch, Ralph
Relativization and Interactive Proof Systems in Parameterized Complexity Theory
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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 | |
| Seminar: | 12th International Symposium on Parameterized and Exact Computation (IPEC 2017) | |
| Issue date: | 2018 | |
| Date of publication: | 02.03.2018 |
