Cost-Optimal Decision Diagrams for Stochastic Boolean Function Evaluation

2026-06-23

AI Summary

This work addresses the cost-aware stochastic Boolean function evaluation problem, where variables have heterogeneous acquisition costs and truth values follow a given probability distribution, with the goal of constructing a deterministic evaluation strategy that minimizes expected cost. The study presents the first practical exact algorithm for this general setting and establishes that the problem is #P-hard and resides in PSPACE. The proposed algorithm employs a branch-and-bound framework enhanced with variable selection heuristics, pruning techniques, and caching mechanisms; additionally, a greedy beam search variant is introduced to balance computational efficiency and solution quality. Experimental results demonstrate strong scalability on random instances, accurately characterize the trade-off between efficiency and accuracy in beam search, and confirm successful application to structured real-world scenarios such as heart disease diagnosis.

Abstract

In many decision-making scenarios, acquiring information incurs different costs. We consider the problem of constructing a deterministic evaluation strategy that minimizes the expected cost of evaluating a propositional formula under variable costs and a probability distribution over truth assignments. We present a branch-and-bound algorithm with variable-selection heuristics, pruning, and caching. To the best of our knowledge, it is the first practical exact algorithm for this level of generality. Experiments on random instances demonstrate scalability and quantify the efficiency-quality trade-off of a greedy beam-search variant. We additionally evaluate a structured heart-disease diagnosis instance. Finally, we prove that the problem is $\#P$-hard and contained in $\mathrm{PSPACE}$.

Problem

• Stochastic Boolean Function Evaluation
• Cost-Optimal Decision Diagrams
• Expected Cost Minimization
• Propositional Formula Evaluation
• Variable Costs

Innovation

• cost-optimal decision diagrams
• stochastic Boolean function evaluation
• branch-and-bound algorithm
• #P-hardness
• variable-cost evaluation