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.
Papers published on a yearly basis
Papers
More filters
17 May 2004
TL;DR: A reduced complexity implementation of a soft Chase algorithm for algebraic soft-decision decoding of Reed-Solomon (RS) codes, based on the recently proposed algorithm of Koetter and Vardy, is presented.
Abstract: A reduced complexity implementation of a soft Chase algorithm for algebraic soft-decision decoding of Reed-Solomon (RS) codes, based on the recently proposed algorithm of Koetter and Vardy, is presented. The reduction in complexity is obtained at the algorithm level by integrating the re-encoding and Chase algorithms and at the architecture level by considering a backup mode which sharply reduces the average computational complexity of the hybrid decoder.
5 citations
13 Nov 2015
TL;DR: It is shown that the lower bound of the complexity of the fulfillment problem of 4 input/output logics is coNP, while the upper bound is either coNP or P\(^{NP}\).
Abstract: Input/output logics are abstract structures designed to represent conditional norms. The complexity of input/output logic has been sparsely developed. In this paper we study the complexity of input/output logics. We show that the lower bound of the complexity of the fulfillment problem of 4 input/output logics is coNP, while the upper bound is either coNP or P\(^{NP}\). (This paper is an extension of a short paper [20] by the same authors.)
5 citations
21 Jan 2006
TL;DR: A new complexity measure for Boolean functions is introduced and has a link to the query algorithms: it stands between both polynomial degree and non-deterministic complexity on one hand and still is a lower bound for deterministic complexity.
Abstract: A new complexity measure for Boolean functions is introduced in this article. It has a link to the query algorithms: it stands between both polynomial degree and non-deterministic complexity on one hand and still is a lower bound for deterministic complexity. Some inequalities and counterexamples are presented and usage in symmetrisation polynomials is considered.
5 citations
01 Jan 1993
TL;DR: This work proves that the Kolmogorov complexity of the weights of neural networks is infinite, and shows that neural networks can be classified into an infinite hierarchy of different computing capabilities.
Abstract: The computational power of neural networks depends on properties of the real numbers used as weights. We focus on networks restricted to compute in polynomial time, operating on boolean inputs. Previous work has demonstrated that their computational power happens to coincide with the complexity classes P and P/poly, respectively, for networks with rational and arbitrary real weights. Here we prove that the crucial concept that characterizes this computational power is the Kolmogorov complexity of the weights, in the sense that, for each bound on this complexity, the networks can solve exactly the problems in a related nonuniform complexity class located between P and P/poly. By proving that the family of such nonuniform classes is infinite, we show that neural networks can be classified into an infinite hierarchy of different computing capabilities.
5 citations
Posted Content•
TL;DR: In this article, the average number of data-movements (and comparisons) made by a $p$-pass Shellsort for any incremental sequence is shown to be O(pn^{1 + 1/p)$ for all $p \leq \log n).
Abstract: We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a $p$-pass Shellsort for any incremental sequence is $\Omega (pn^{1 + 1/p)$ for all $p \leq \log n$. Using similar arguments, we analyze the average-case complexity of several other sorting algorithms.
5 citations