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Relativization and Interactive Proof Systems in Parameterized Complexity Theory Bottesch, Ralph Parameterized complexity Relativization Interactive Proof Systems 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ralph Bottesch 2018 Is Part Of LIPIcs, Volume 89, 12th International Symposium on Parameterized and Exact Computation (IPEC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.IPEC.2017.9 urn:nbn:de:0030-drops-85715 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2017.9 eng https://creativecommons.org/licenses/by/3.0/legalcode