Uniformly defining complexity classes of functions

  • Sven Kosub
  • Heinz Schmitz
  • Heribert Vollmer
Complexity IV
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1373)


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).


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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Sven Kosub
    • 1
  • Heinz Schmitz
    • 1
  • Heribert Vollmer
    • 1
  1. 1.Theoretische InformatikUniversität WürzburgWürzburgGermany

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