arXiv subjects
Publications and source records attributed to Tonguç Ünlüyurt.
This review aims to provide a comprehensive update on the progress made on the Sequential Testing problem (STP) in the last 20 years after the review, [1] was published. Many studies have provided new theoretical results, extensions of the problem, and new applications. In this review, we pinpoint the main results and discuss the relations between the problems studied. We also provide possible research directions for the problem.
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.