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Uniformly defining complexity classes of functions

  • Complexity IV
  • Conference paper
  • First Online:
STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

We introduce a general framework for the definition of function classes. Our model, which is based on polynomial time nondeterministic Turing transducers, allows uniform characterizations of FP, FPNP, counting classes (#·P, #·NP, #·coNP, GapP, GapPNP), optimization classes (max·P, min·P, max·NP, min·NP), promise classes (NPSV, #few·P, c#·P), multivalued classes (FewFP, NPMV) and many more. Each such class is defined in our model by a certain family of functions. We study a reducibility notion between such families, which leads to a necessary and sufficient criterion for relativizable inclusion between function classes. As it turns out, this criterion is easily applicable and we get as a consequence e.g. that there are oracles A, B, such that min.PA \(\nsubseteq\) #·NPA, and max.NPB \(\nsubseteq\) c#·coNPB (note that no structural consequences are known to follow from the corresponding positive inclusions).

Supported by the Deutsche Forschungsgemeinschaft (DFG), grant Wa 847/1-2.

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Authors and Affiliations

  1. Theoretische Informatik, Universität Würzburg, Am Exerzierplatz 3, 97072, Würzburg, Germany

    Sven Kosub, Heinz Schmitz & Heribert Vollmer

Authors
  1. Sven Kosub
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  2. Heinz Schmitz
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  3. Heribert Vollmer
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Editor information

Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Kosub, S., Schmitz, H., Vollmer, H. (1998). Uniformly defining complexity classes of functions. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028595

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  • DOI: https://doi.org/10.1007/BFb0028595

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

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