Cost-Optimal Decision Diagrams for Stochastic Boolean Functions

In many decision-making scenarios, the process of acquiring information comes with varying costs. This research addresses the challenge of creating a deterministic evaluation strategy that minimizes the expected cost when evaluating a propositional formula. The problem accounts for both variable costs associated with information acquisition and a probability distribution over possible truth assignments. The paper introduces a branch-and-bound algorithm designed to solve this complex problem. This algorithm incorporates several advanced techniques, including variable-selection heuristics, pruning strategies, and caching mechanisms, making it the first practical exact algorithm capable of handling this level of generality. Experimental evaluations on random instances demonstrate the algorithm's scalability and quantify the trade-offs between efficiency and quality when compared to a greedy beam-search variant. The framework was also tested on a structured heart-disease diagnosis instance. Furthermore, the authors prove that the problem is #P-hard and contained within PSPACE, highlighting its computational complexity.