Parameterized Complexity of Fixed Variable Logics

Authors Christoph Berkholz, Michael Elberfeld

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Christoph Berkholz
Michael Elberfeld

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Christoph Berkholz and Michael Elberfeld. Parameterized Complexity of Fixed Variable Logics. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 109-120, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


We study the complexity of model checking formulas in first-order logic parameterized by the number of distinct variables in the formula. This problem, which is not known to be fixed-parameter tractable, resisted to be properly classified in the context of parameterized complexity. We show that it is complete for a newly-defined complexity class that we propose as an analog of the classical class PSPACE in parameterized complexity. We support this intuition by the following findings: First, the proposed class admits a definition in terms of alternating Turing machines in a similar way as PSPACE can be defined in terms of polynomial-time alternating machines. Second, we show that parameterized versions of other PSPACE-complete problems, like winning certain pebble games and finding restricted resolution refutations, are complete for this class.
  • Parameterized complexity
  • polynomial space
  • first-order logic
  • pebble games
  • regular resolutions


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