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Complete Distributional Problems, Hard Languages, and Resource-Bounded Measure
 

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

  

Source: Aduri, Pavan - Department of Computer Science, Iowa State University

 

Collections: Computer Technologies and Information Sciences