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Relativization and Interactive Proof Systems in Parameterized Complexity Theory

Author Ralph Bottesch

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Ralph Bottesch

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Ralph Bottesch. Relativization and Interactive Proof Systems in Parameterized Complexity Theory. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 9:1-9:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.IPEC.2017.9

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.

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Keywords
  • Parameterized complexity
  • Relativization
  • Interactive Proof Systems

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