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Parameterized Random Complexity

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Abstract

The classes W[P] and W[1] are parameterized analogues of NP in that they can be characterized by machines with restricted existential nondeterminism. These machine characterizations give rise to two natural notions of parameterized randomized algorithms that we call W[P]-randomization and W[1]-randomization. This paper develops the corresponding theory.

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Notes

  1. The authors do not know whether p-#MC(LFP1) is # W[P]-complete.

  2. Recall a function f:ℕ→ℕ is time-constructible if and only if there is a (deterministic) Turing machine that on every x halts after exactly f(|x|) many steps.

  3. Concepts of tractability for listing problems have been introduced in [45].

  4. DP is sometimes written DP and comprises the differences of NP problems; [26, Exercise 16.04] introduces a parameterized ‘stratification’ of this class.

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Acknowledgements

We thank again Jörg Flum, the advisor of our PhD Theses. The second author thanks the John Templeton Foundation for its support under Grant #13152, The Myriad Aspects of Infinity and the FWF (Austrian Research Fund) for its support under Grant P23989-N13.

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Authors and Affiliations

  1. Escuela de Matemáticas, Universidad industrial de Santander, Bucaramanga, Colombia

    Juan Andrés Montoya

  2. Kurt Gödel Research Center, University of Vienna, Vienna, Austria

    Moritz Müller

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  1. Juan Andrés Montoya
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  2. Moritz Müller
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Correspondence to Moritz Müller.

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Montoya, J.A., Müller, M. Parameterized Random Complexity. Theory Comput Syst 52, 221–270 (2013). https://doi.org/10.1007/s00224-011-9381-0

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