 
Summary: Complete Distributional Problems, Hard
Languages, and ResourceBounded Measure
A. Pavan
Alan L. Selman
Department of Computer Science
University at Buffalo
Buffalo, NY 14260
Abstract
We say that a distribution µ is reasonable if there exists a constant s 0 such
that µ({x  x n}) = ( 1
ns ). We prove the following result, which suggests that all
DistNPcomplete problems have reasonable distributions.
If NP contains a DTIME(2n
)biimmune set, then every DistNPcomplete
set has a reasonable distribution.
It follows from work of Mayordomo [May94] that the consequent holds if the pmeasure
of NP is not zero.
Cai and Selman [CS96] defined a modification and extension of Levin's notion of
average polynomial time to arbitrary timebounds and proved that if L is Pbiimmune,
then L is distributionally hard, meaning, that for every polynomialtime computable
