Random-Like Testing of Very Large Scale Integration Circuit

A new approach to improve the test efficiency of random testing is presented in this paper. In conventional random testing, each test pattern is selected randomly regardless of the tests previously generated. This paper introduces the concept of random like testing. The method provided appears to have the same concepts as used in random testing,but actually takes an opposite way to it in order to improve the efficiency of random testing.In a random like testing sequence, the total distance among all test patterns is chosen to be maximal so that the fault sets detected by one test pattern are as different as possible from that detected by the tests previously applied. The procedure to construct a random like testing sequence (RLTS) is described in detail. Theorems to justify the effectiveness and usefulness of the procedure presented are developed. Experimental results on benchmark circuits as well as on other circuit are also given to evaluate the performance of the new approach.

Industrial Green Spatial Pattern Evolution of Yangtze River Economic Belt in China

We use the directional slacks-based measure of efficiency and inverse distance weighting method to analyze the spatial pattern evolution of the industrial green total factor productivity of 108 cities in the Yangtze River Economic Belt in 2003–2013.Results show that both the subprime mortgage crisis and ‘the new normal' had significant negative effects on productivity growth,leading to the different spatial patterns between 2003–2008 and 2009–2013.Before 2008,green poles had gathered around some capital cities and formed a tripartite pattern,which was a typical core-periphery pattern.Due to a combination of the polarization and the diffusion effects,capital cities became the growth poles and ‘core' regions,while surrounding areas became the ‘periphery'.This was mainly caused by the innate advantage of capital cities and ‘the rise of central China' strategy.After 2008,the tripartite pattern changed to a multi-poles pattern where green poles continuously and densely spread in the midstream and downstream areas.This is due to the regional difference in the leading effect of green poles.The leading effect of green poles in midstream and downstream areas has changed from polarization to diffusion,while the polarization effect still leads in the upstream area.

Approximation for counts of head runs

In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein's method and coupling.

Approximation for Counts of 2-runs in a Two State Markov Chain

We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW. The error estimate obtained herein improves the corresponding result in previous literatures.