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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04 Jul 1994
TL;DR: It is shown that under reasonable assumptions the complexity can increase only if the complexity of all the uni-modal fragments is below PSPACE.
Abstract: We prove general theorems about the relationship between the complexity of multi-modal logics and the complexity of their uni-modal fragments Halpern and Moses (1985) show that the complexity of a multi-modal logic without any interaction between the modalities may be higher than the complexity of the individual fragments We show that under reasonable assumptions the complexity can increase only if the complexity of all the uni-modal fragments is below PSPACE In addition, we completely characterize what happens if the complexity of all fragments is below PSPACE >
12 citations
TL;DR: This result disproved the conjecture that there exists a trade-off between the linear complexity and the k-error linear complexity of a periodic sequence by Ding by considering the orders of the divisors of xN-1 over \BBF q.
Abstract: Niederreiter showed that there is a class of periodic sequences which possess large linear complexity and large k-error linear complexity simultaneously. This result disproved the conjecture that there exists a trade-off between the linear complexity and the k-error linear complexity of a periodic sequence by Ding By considering the orders of the divisors of xN-1 over \BBF q, we obtain three main results which hold for much larger k than those of Niederreiter : a) sequences with maximal linear complexity and almost maximal k-error linear complexity with general periods; b) sequences with maximal linear complexity and maximal k -error linear complexity with special periods; c) sequences with maximal linear complexity and almost maximal k-error linear complexity in the asymptotic case with composite periods. Besides, we also construct some periodic sequences with low correlation and large k -error linear complexity.
12 citations
01 Jan 2013
TL;DR: A combination framework for the automated polynomial complexity analysis of term rewrite systems is presented, which covers both derivational and runtime complexity analysis, and is employed as theoretical foundation in the automated complexity tool TCT.
Abstract: In this paper we present a combination framework for the automated polynomial complexity analysis of term rewrite systems. The framework covers both derivational and runtime complexity analysis, and is employed as theoretical foundation in the automated complexity tool TCT. We present generalisations of powerful complexity techniques, notably a generalisation of complexity pairs and (weak) dependency pairs. Finally, we also present a novel technique, called dependency graph decomposition, that in the dependency pair setting greatly increases modularity.
12 citations
15 Dec 2008
TL;DR: It is shown that the "black-box" approach to convert quantum query algorithms into communication protocols by Buhrman-Cleve-Wigderson [STOC'98] is optimal even in the unbounded-error setting, and a tight multiplicative θ(logn) separation between quantum and classical query complexity in this setting for a partial Boolean function.
Abstract: This work studies the quantum query complexity of Boolean functions in an unbounded-error scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We first show that, just as in the communication complexity model, the unbounded-error quantum query complexity is exactly half of its classical counterpart for any (partial or total) Boolean function. Next, connecting the query and communication complexity results, we show that the "black-box" approach to convert quantum query algorithms into communication protocols by Buhrman-Cleve-Wigderson [STOC'98] is optimal even in the unbounded-error setting. We also study a related setting, called the weakly unbounded-error setting. In contrast to the case of communication complexity, we show a tight multiplicative θ(logn) separation between quantum and classical query complexity in this setting for a partial Boolean function.
12 citations
06 May 2001
TL;DR: It is shown that maximum likelihood (ML) detection can be carried out by 'relaxing' the associated integer programming problem to a semidetinite-programming problem, which leads to a detector of polynomial complexity.
Abstract: A semidefinite-programming based multiuser detector is proposed. It is shown that maximum likelihood (ML) detection can be carried out by 'relaxing' the associated integer programming problem to a semidetinite-programming problem, which leads to a detector of polynomial complexity. Computer simulations presented demonstrate that the proposed detector offers near-optimal performance with much reduced computational complexity compared with that of the ML detector.
12 citations