Probabilistic Satisfiability

Given an arbitrary boolean expression, satisfiability (SAT) refers to the task of finding a truth assignment to the boolean variables that makes the expression true. For example, the boolean expression a & b is true if and only if the boolean variables a and b are true. Satisfiability is of interest to the logic, operations research, and computational complexity communities. Due to the emphasis of the logic community, satisfiability algorithms tend to be sound and complete. However, a current trend is to relax some of these requirements. For example, recent work on satisfiability examines incomplete algorithms (Spears, 1990; Young and Reel, 1990; Mitchell, 1992; Gu, 1992). These algorithms are sound in that, if they discover satisfying assignments, these assignments are correct. However, if a satisfying assignment does not exist, the algorithm will never prove this. Furthermore, there is no guarantee that the algorithm will find a satisfying assignment if one exists (i.e., incompleteness). Despite these obvious drawbacks, such algorithms are advantageous for certain classes of problems (Mitchell, 1992).