Stable Independance and Complexity of Representation

The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from which any other statement can be generated by means of the axioms; the cardinality of this set is taken to indicate the complexity of the relation. Building upon the idea of dominance, we introduce the concept of stability to provide for a more compact representation of independence. We give an associated algorithm for establishing such a representation.We show that, with our concept of stability, many independence relations are found to be of lower complexity than with existing representations.