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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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TL;DR: This paper defines and study probabilistic complexity classes, survey the basic results, and show how they relate to the notion of randomized algorithms.
Abstract: In this paper we give an introduction to the connection between complexity theory and the study of randomized algorithms. In particular, we will define and study probabilistic complexity classes, survey the basic results, and show how they relate to the notion of randomized algorithms.
1 citations
24 Oct 2004
TL;DR: An algorithm which, given a constant c and an infinite binary sequence s with period lscr=2n, computes the minimum number k of errors needed over a period of s for bringing the linear complexity of s below c.
Abstract: The linear Games-Chan algorithm for computing the linear complexity c(s) of a binary sequence s of period l = 2n requires the knowledge of the full sequence, while the quadratic Berlekamp-Massey algorithm only requires knowledge of 2c(s) terms We show that we can modify the Games-Chan algorithm so that it computes the complexity in linear time knowing only 2c(s) terms The algorithms of Stamp-Martin and Lauder-Paterson can also be modified, without loss of efficiency, to compute analogues of the k-error linear complexity and of the error linear complexity spectrum for finite binary sequences viewed as initial segments of infinite sequences with period a power of two Lauder and Paterson apply their algorithm to decoding binary repeated-root cyclic codes of length l = 2n in ${\mathcal O}(\ell({\rm log}_{2}\ell)^2)$ time We improve on their result, developing a decoding algorithm with ${\mathcal O}(\ell)$ bit complexity
1 citations
TL;DR: Asymptotically optimal bounds are established in terms of q for the number of elements f that are relatively prime with g and for the average degree of g when the highest degree polynomial g is fixed.
Abstract: We analyze the behavior of the Euclidean algorithm applied to pairs (g,f) of univariate nonconstant polynomials over a finite field F_q of q elements when the highest-degree polynomial g is fixed. Considering all the elements f of fixed degree, we establish asymptotically optimal bounds in terms of q for the number of elements f which are relatively prime with g and for the average degree of gcd(g,f). The accuracy of our estimates is confirmed by practical experiments. We also exhibit asymptotically optimal bounds for the average-case complexity of the Euclidean algorithm applied to pairs (g,f) as above.
1 citations
01 Sep 1990
TL;DR: A formal approach to the evaluation and comparison of text-manipulation systems is discussed, based on T-spaces, a class of transitive mathematical models, in terms of which the editable sets are exactly the recursively enumerable ones.
Abstract: A formal approach to the evaluation and comparison of text-manipulation systems is discussed. It is based on T-spaces, a class of transitive mathematical models, in terms of which the editable sets are exactly the recursively enumerable ones. Evaluation relies on the associated time/space complexity measures, some of which reflect the complexity of a system as a unity, while others are independent of the computational complexities of the text-manipulation operations. For all types of complexity measures linear speedup/compression theorems hold. >
1 citations
TL;DR: For several different algebraic structures S, this work studies the computational complexity of such problems as determining, for a system of equations on S, how to solve the inequality of the entailments of Euler's inequality.
Abstract: For several different algebraic structures S, we study the computational complexity of such problems as determining, for a system of equations on S,
1 citations