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.

Computing the k-error 2-adic complexity of 2 n -periodic sequence based on genetic algorithm

Abstract: Sequences generated by feedback with carry shift registers (FCSR) have been extensively concerned for their as excellent randomness as the sequences generated by linear feedback shift registers (LFSR). 2-adic complexity is of fundamental importance as measure index on the security of cryptographic sequence. A good random sequence should not only have a high 2-adic complexity but also a few bit changed can not cause a significant decrease of the 2- adic complexity. This requirement leads to the concept of k-error 2-adic complexity. However it is a difficult problem to compute the k-error 2-adic complexity based on the traditional method in algebraic analysis. Considering that it is an optimization problem and the genetic algorithm is good at solving these problems, we investigate the genetic algorithm to compute the k-error 2-adic complexity of 2n-periodic sequences. The experiments show that we can get the approximate values very close to the exact value.

Complexity-distortion tradeoffs in variable complexity 2-D DCT

Abstract: Variable complexity algorithms (VCAs) (i.e. algorithms which take a variable, input-dependent amount of time to complete a task) have been proposed to reduce the average computational complexity of compression algorithms for images and videos. In this paper we introduce a new 2-D variable-complexity DCT that can be used to replace the regular discrete cosine transform (DCT), if only a part of DCT coefficients need to be computed. Consequently, the computational complexity of the DCT can be reduced at the cost in degradation of the reconstructed image quality. We investigate fine-grained complexity-distortion tradeoffs for the proposed variable-complexity, separable DCT (VS-DCT). The evaluation includes a theoretical computational complexity analysis of the VS-DCT in terms of the number of additions and multiplications (note in this paper computational complexity does not refer to the polynomial order of operations) and empirical complexity-distortion curves of the VS-DCT running on two distinct platforms, including a desktop personal computer and an embedded system. The results of evaluation show that our VS-DCT can reduce the computational complexity of a regular DCT by up to 10% for every 3dB decrease in the PSNR (peak signal-to-noise ratio) of the reconstructed images.

An Algorithm for Computing $m$-Tight Error Linear Complexity of Sequences over $GF(p^{m})$ with Period $p^{m}$

Abstract: The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity profile, the notion of $m$-tight error linear complexity is presented. An efficient algorithm for computing $m$-tight error linear complexity is derived from the algorithm for computing $k$-error linear complexity of sequences over GF($p^{m}$) with period $p^n$, where $p$ is a prime. The validity of the algorithm is shown. The algorithm is also realized with C language, and an example is presented to illustrate the algorithm.