  In a previous paper [Pearl and Verma, 1991] we presented an algorithm for
extracting causal influences from independence information, where a causal
influence was defined as the existence of a directed arc in all minimal causal
models consistent with the data. In this paper we address the question of
deciding whether there exists a causal model that explains ALL the observed
dependencies and independencies. Formally, given a list M of conditional
independence statements, it is required to decide whether there exists a
directed acyclic graph (dag) D that is perfectly consistent with M, namely,
every statement in M, and no other, is reflected via dseparation in D. We
present and analyze an effective algorithm that tests for the existence of such
a day, and produces one, if it exists.
