Average-case intractability vs. worst-case intractability

Authors:
Johannes Köbler;Rainer Schuler
Affiliations:
Institut für Informatik, Humboldt-Universität zu Berlin, D-10099 Berlin, Germany;Abt. Theoretische Informatik, Universität Ulm, Oberer Eselsberg, D-89069 Ulm, Germany
Venue:
Information and Computation
Year:
2004

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Abstract

We show that not all sets in NP (or other levels of the polynomial-time hierarchy) have efficient average-case algorithms unless the Arthur-Merlin classes MA and AM can be derandomized to NP and various subclasses of P/poly collapse to P. Furthermore, other complexity classes like P(PP) and PSPACE are shown to be intractable on average unless they are easy in the worst case.