  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 arc -
consistency.This allows the synthesis OF belief networks FOR which belief
propagation IS useless ON one hand, AND focuses the investigation OF classes OF
belief network FOR which belief propagation may be zero - complete.Finally, ALL
the above conclusions apply also TO Generalized belief propagation algorithms
that extend loopy belief propagation AND allow a crisper understanding OF their
power.
