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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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Proceedings ArticleDOI
01 Sep 2007
TL;DR: The preliminary experiments show that the genetic algorithm approach is suitable to the problem and that a good scheme would use a medium sized population, an elitist type of selection, a special design of the two point random crossover and a standard random mutation.
Abstract: Some cryptographical applications use pseudorandom sequences and require that the sequences are secure in the sense that they cannot be recovered by only knowing a small amount of consecutive terms. Such sequences should therefore have a large linear complexity and also a large k-error linear complexity. Efficient algorithms for computing the k-error linear complexity of a sequence over a finite field only exist for sequences of period equal to a power of the characteristic of the field. It is therefore useful to find a general and efficient algorithm to compute a good approximation of the k-error linear complexity. In this paper we investigate the design of a genetic algorithm to approximate the k-error linear complexity of a sequence. Our preliminary experiments show that the genetic algorithm approach is suitable to the problem and that a good scheme would use a medium sized population, an elitist type of selection, a special design of the two point random crossover and a standard random mutation. The algorithm outputs an approximative value of the k-error linear complexity which is on average only 19.5% higher than the exact value. This paper intends to be a proof of concept that the genetic algorithm technique is suitable for the problem in hand and future research will further refine the choice of parameters.

9 citations

Book ChapterDOI
20 Apr 2015
TL;DR: Free is presented, an effective and efficient RCE solution to explore rare categories of arbitrary shapes on a linear time complexity w.r.t. data set size and results on both synthetic and real data sets verify the effectiveness and efficiency of this approach.
Abstract: Rare Category Exploration (in short as RCE) discovers the remaining data examples of a rare category from a seed. Approaches to this problem often have a high time complexity and are applicable to rare categories with compact and spherical shapes rather than arbitrary shapes. In this paper, we present FREE an effective and efficient RCE solution to explore rare categories of arbitrary shapes on a linear time complexity w.r.t. data set size. FREE firstly decomposes a data set into equal-sized cells, on which it performs wavelet transform and data density analysis to find the coarse shape of a rare category, and refines the coarse shape via an M\(k\)NN based metric. Experimental results on both synthetic and real data sets verify the effectiveness and efficiency of our approach.

9 citations

Journal ArticleDOI
TL;DR: This work replaces the determinant in geometric complexity theory with the trace of a symbolic matrix power and proves that in this homogeneous formulation there are no orbit occurrence obstructions that prove even superlinear lower bounds on the complexity of the permanent.
Abstract: Valiant's famous determinant versus permanent problem is the flagship problem in algebraic complexity theory. Mulmuley and Sohoni (2001, 2008) [23] , [24] introduced geometric complexity theory, an approach to study this and related problems via algebraic geometry and representation theory. Their approach works by multiplying the permanent polynomial with a high power of a linear form (a process called padding) and then comparing the orbit closures of the determinant and the padded permanent. This padding was recently used heavily to show negative results for the method of shifted partial derivatives (Efremenko et al., 2016 [6] ) and for geometric complexity theory (Ikenmeyer and Panova, 2016 [17] and Burgisser et al., 2016 [3] ), in which occurrence obstructions were ruled out to be able to prove superpolynomial complexity lower bounds. Following a classical homogenization result of Nisan (1991) [25] we replace the determinant in geometric complexity theory with the trace of a symbolic matrix power. This gives an equivalent but much cleaner homogeneous formulation of geometric complexity theory in which the padding is removed. This radically changes the representation theoretic questions involved to prove complexity lower bounds. We prove that in this homogeneous formulation there are no orbit occurrence obstructions that prove even superlinear lower bounds on the complexity of the permanent. Interestingly—in contrast to the determinant—the trace of a symbolic matrix power is not uniquely determined by its stabilizer.

9 citations

Journal ArticleDOI
TL;DR: A notion of size and complexity for strategies in sequential games is defined, which defines a notion of complexity for PCF functions, and the corresponding higher-order polynomial time complexity class contains BFF.

8 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
20216
202010
20199
201810
201732