has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL) about forty years ago, this area has seen active research effort with many interesting contributions that have culminated in state-of-the-art SAT solvers today being able to handle problem instances with thousands, and in same cases even millions, of variables. In this paper we examine some of the main ideas along this passage that have led to our current capabilities. Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. For the most part, we focus on techniques within the basic DPLL search framework, but also briefly describe other approaches and look at some possible future research directions. 1.

This paper considers the fault detection problem for a single fault in a single MOS channel-connected subcircuit. We identify the following three decision sub-problems : (i) decide if a test vector exists; (ii) decide if an initializing vector exists; and (iii) decide if a test pair is robust. We prove that each of these problems is NP \Gamma complete. More importantly, we prove that the first two remain NP \Gamma complete for the simplest subcircuit design styles, namely series/parallel nMOS or CMOS logic gates. The third subproblem is shown to be of linear complexity for a CMOS logic gate with a stuck-open fault. We illustrate that a test pair that is not robust may contain a robust sub-test pair, and give a necessary and sufficient condition for this to happen in CMOS logic gates. This leads to a linear-time algorithm for CMOS logic gates which tests for robustness and, if possible, derives a robust test pair from a possibly non-robust pair. The implications of these complexity resu...