 
Summary: Submitted to the Symposium on Theoretical Aspects of Computer Science
www.stacsconf.org
COLLAPSING AND SEPARATING COMPLETENESS NOTIONS UNDER
AVERAGECASE AND WORSTCASE HYPOTHESES
XIAOYANG GU 1
AND JOHN M. HITCHCOCK 2
AND A. PAVAN 3
1
LinkedIn Corporation
2
Department of Computer Science, University of Wyoming
3
Department of Computer Science, Iowa State University
Abstract. This paper presents the following results on sets that are complete for NP.
(i) If there is a problem in NP that requires 2n(1)
time at almost all lengths, then every many
one NPcomplete set is complete under lengthincreasing reductions that are computed by
polynomialsize circuits.
(ii) If there is a problem in coNP that cannot be solved by polynomialsize nondeterministic
circuits, then every manyone complete set is complete under lengthincreasing reductions
