Topic
Average-case complexity
About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.
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03 Jan 1991TL;DR: New lower bounds are presented that give (1) randomization is more powerful than determinism in $k-round protocols, and (2) an explicit function which exhibits an exponential gap between its $k$ and $(k-1)$-round randomized complexity.
Abstract: The $k$-round two-party communication complexity was studied in the deterministic model by [14] and [4] and in the probabilistic model by [20] and [6]. We present new lower bounds that give (1) randomization is more powerful than determinism in $k$-round protocols, and (2) an explicit function which exhibits an exponential gap between its $k$ and $(k-1)$-round randomized complexity. We also study the three party communication model, and exhibit an exponential gap in 3-round protocols that differ in the starting player. Finally, we show new connections of these questions to circuit complexity, that motivate further work in this direction.
116 citations
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27 Aug 2008
TL;DR: This paper discusses decision problems in Public Key Cryptography, the Asymptotically Dominant Properties of Cryptanalysis, and length-Based and Quotient Attacks.
Abstract: Background on Groups, Complexity, and Cryptography.- Background on Public Key Cryptography.- Background on Combinatorial Group Theory.- Background on Computational Complexity.- Non-commutative Cryptography.- Canonical Non-commutative Cryptography.- Platform Groups.- Using Decision Problems in Public Key Cryptography.- Generic Complexity and Cryptanalysis.- Distributional Problems and the Average-Case Complexity.- Generic Case Complexity.- Generic Complexity of NP-complete Problems.- Asymptotically Dominant Properties and Cryptanalysis.- Asymptotically Dominant Properties.- Length-Based and Quotient Attacks.
116 citations
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TL;DR: An O(log n ) time wait-free approximate agreement algorithm is presented; the complexity of this algorithm is within a small constant of the lower bound.
Abstract: The time complexity of wait-free algorithms in “normal” executions, where no failures occur and processes operate at approximately the same speed, is considered. A lower bound of log n on the time complexity of any wait-free algorithm that achieves approximate agreement among n processes is proved. In contrast, there exists a non-wait-free algorithm that solves this problem in constant time. This implies an O(log n) time separation between the wait-free and non-wait-free computation models. On the positive side, we present an O(log n) time wait-free approximate agreement algorithm; the complexity of this algorithm is within a small constant of the lower bound.
114 citations
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TL;DR: The Smyth-completeness of the complexity space and the compactness of closed complexity spaces which possess a (complexity) lower bound have been investigated in this paper, where the complexity analysis of Divide and Conquer algorithms has been studied.
113 citations