On functions and relations

Authors:
André Große;Harald Hempel
Affiliations:
Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany
Venue:
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Year:
2003

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Abstract

We present a uniform definition for classes of single- and multi-valued functions. We completely analyze the inclusion structure of function classes. In order to compare classes of multi-valued and single-valued functions with respect to the existence of refinements we extend the so called operator method [VW93,HW00] to make it applicable to such cases. Our approach sheds new light on well-studied classes like NPSV and NPMV, allows to give simpler proofs for known results, and shows that the spectrum of function classes closely resembles the spectrum of well-known complexity classes.