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Some Results on Average-Case Hardness within the Polynomial Hierarchy
 

Summary: Some Results on Average-Case Hardness within
the Polynomial Hierarchy
A. Pavan1
, Rahul Santhanam2
, and N. V. Vinodchandran3
1
Department of Computer Science, Iowa State University
2
Department of Computer Science, Simon Fraser University
3
Department of Computer Science and Engineering, University of Nebraska-Lincon
Abstract. We prove several results about the average-case complex-
ity of problems in the Polynomial Hierarchy (PH). We give a connec-
tion among average-case, worst-case, and non-uniform complexity of op-
timization problems. Specifically, we show that if PNP
is hard in the
worst-case then it is either hard on the average (in the sense of Levin)
or it is non-uniformly hard (i.e. it does not have small circuits).
Recently, Gutfreund, Shaltiel and Ta-Shma (IEEE Conference on Com-
putational Complexity, 2005) showed an interesting worst-case to average-

  

Source: Aduri, Pavan - Department of Computer Science, Iowa State University
Variyam, Vinodchandran N. - Department of Computer Science and Engineering, University of Nebraska-Lincoln

 

Collections: Computer Technologies and Information Sciences