Sequential testing of series parallel systems

In this thesis, we study the sequential testing problem of 3-level deep Series Parallel systems (SPS). We assess the performance of depth-first permutation (DFP) algorithm that has been proposed in the literature. DFP is optimal for 1-level deep, 2-level deep SPSs and 3-level deep SPSs that consist of identical components. It can be used to test general SPSs. We report the first computational results regarding the performance of DFP for 3-level deep SPSs by comparing its performance with a dynamic version of DFP and a hybrid simulated annealing-tabu search algorithm that we developed. In order to implement the algorithms, we propose an efficient method to compute the expected cost of a permutation strategy. The results of computational experiments for this algorithm and other algorithms proposed in the literature are reported

Evaluation of DNF formulas

Stochastic Boolean Function Evaluation (SBFE) is the problem of determining the value of a given Boolean function $f$ on an unknown input $x$, when each bit of $x_i$ of $x$ can only be determined by paying a given associated cost $c_i$. Further, $x$ is drawn from a given product distribution: for each $x_i$, $Prob[x_i=1] = p_i$, and the bits are independent. The goal is to minimize the expected cost of evaluation. Stochastic Boolean Function Evaluation (SBFE) is the problem of determining the value of a given Boolean function $f$ on an unknown input $x$, when each bit of $x_i$ of $x$ can only be determined by paying a given associated cost $c_i$. Further, $x$ is drawn from a given product distribution: for each $x_i$, $Prob[x_i=1] = p_i$, and the bits are independent. The goal is to minimize the expected cost of evaluation. In this paper, we study the complexity of the SBFE problem for classes of DNF formulas. We consider both exact and approximate versions of the problem for subclasses of DNF, for arbitrary costs and product distributions, and for unit costs and/or the uniform distribution