Some Relationships between the FOIES and S1 Arity Hierarchies

A rst order incremental evaluation system foies uses rst order queries to maintain a database view which is de ned by a non rst order query some auxiliary relations views may also need to be maintained similarly In foies monadic auxiliary relations were known to be strictly weaker than binary ones however it is open whether k ary auxiliary relations are strictly weaker than k ary ones for k if we limit the arity of the input relations to be at most k In the full version of the PODS paper DS b which will appear in JCSS it is shown that the answer to this question is positive if we do not limit the arity of the input relations It appears hard to generalize the techniques used for current separation results to solve the above problem On the other hand the arity hierarchy of was shown to be strict