In this lecture we discuss how to derandomize algorithms. We will see a brute force algorithm (enumeration) for derandomization. We will also see that some random algorithms do not need true randomness. Specifically, we will see an example where only pairwise random bits are needed. Next, we will see how we can generate pairwise random values and how this conservation on the amount of randomnes...

In this paper, we will discuss the concept of almost sure convergence for specic groups of fuzzyrandom variables. For this purpose, we use the type of generalized Chebyshev inequalities.Moreover, we show the concept of almost sure convergence of weighted average pairwise NQDof fuzzy random variables.

Let {Xn, n ≥ 1} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums 1 g(n) ∑n i=1 Xi h(i) of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law ...