Results 1 
3 of
3
On the Theory of Average Case Complexity
 Journal of Computer and System Sciences
, 1997
"... This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works [Levin 84, Gurevich 87, Venkatesan and Levin 88] have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. ..."
Abstract

Cited by 108 (7 self)
 Add to MetaCart
This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works [Levin 84, Gurevich 87, Venkatesan and Levin 88] have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. Our results include: ffl the equivalence of search and decision problems in the context of average case complexity; ffl an initial analysis of the structure of distributionalNP (i.e. NP problems coupled with "simple distributions") under reductions which preserve average polynomialtime; ffl a proof that if all of distributionalNP is in average polynomialtime then nondeterministic exponentialtime equals deterministic exponential time (i.e., a collapse in the worst case hierarchy); ffl definitions and basic theorems regarding other complexity classes such as average logspace. An exposition of the basic definitions suggested by Levin and suggestions for some alternative definitions ...
The Round Complexity of Secure Protocols
, 1990
"... ) Donald Beaver Harvard University Silvio Micali y MIT Phillip Rogaway y MIT Abstract In a network of n players, each player i having private input x i , we show how the players can collaboratively evaluate a function f(x 1 ; : : : ; xn ) in a way that does not compromise the privacy of the pla ..."
Abstract

Cited by 93 (2 self)
 Add to MetaCart
) Donald Beaver Harvard University Silvio Micali y MIT Phillip Rogaway y MIT Abstract In a network of n players, each player i having private input x i , we show how the players can collaboratively evaluate a function f(x 1 ; : : : ; xn ) in a way that does not compromise the privacy of the players' inputs, and yet requires only a constant number of rounds of interaction. The underlying model of computation is a complete network of private channels, with broadcast, and a majority of the players must behave honestly. Our solution assumes the existence of a oneway function. 1 Introduction Secure function evaluation. Assume we have n parties, 1; : : : ; n; each party i has a private input x i known only to him. The parties want to correctly evaluate a given function f on their inputs, that is to compute y = f(x 1 ; : : : ; xn ), while maintaining the privacy of their own inputs. That is, they do not want to reveal more than the value y implicitly reveals. Secure function evaluat...
On the Theory of Average Case Complexity Shai BenDavid y
"... This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works [Levin 84, Gurevich 87,Venkatesan and Levin 88] have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. ..."
Abstract
 Add to MetaCart
This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works [Levin 84, Gurevich 87,Venkatesan and Levin 88] have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. Our results include: the equivalence of search and decision problems in the context of average case complexity� an initial analysis of the structure of distributionalNP (i.e. NP problems coupled with \simple distributions&quot;) under reductions which preserve average polynomialtime� a proof that if all of distributionalNP is in average polynomialtime then nondeterministic exponentialtime equals deterministic exponential time (i.e., a collapse in the worst case hierarchy)� de nitions and basic theorems regarding other complexity classes suchasaverage logspace. An exposition of the basic de nitions suggested by Levin and suggestions for some alternative de nitions are provided as well. Remark: This version seems to be a prepublication draft from 1989. Abetterversion has