Abstract
In non-ergodic belief networks the posterior belief of many queries given evidence may become zero. The paper shows that when belief propagation is applied iteratively over arbitrary networks (the so called, iterative or loopy belief propagation (IBP)) it is identical to an arc-consistency algorithm relative to zero-belief queries (namely assessing zero posterior probabilities). This implies that zero-belief conclusions derived by belief propagation converge and are sound. More importantly, it suggests that the inference power of IBP is as strong and as weak as that of arcconsistency. This allows the synthesis of belief networks for which belief propagation is useless on one hand, and focuses the investigation on classes of belief networks for which belief propagation may be zero-complete. Finally, all the above conclusions apply also to Generalized belief propagation algorithms that extend iterative belief propagation and allow a crisper understanding of their power.