Separating Auxiliary Arity Hierarchy of First-order Incremental Evaluation Using (3k+1)-ary Input Relations

1 The Main Result A rst-order incremental evaluation system (foies) uses rst-order queries to maintain a database view which is deened by a non-rst-order query; some auxiliary relations (views) may also need to be maintained similarly. In 7] it was shown that using (k?1)-ary auxiliary relations is strictly less powerful than using k-ary ones, using a reduction to a result by Cai 3] on help bits. However, that separation was achieved using queries having input relations of arity at least 6k. In this note we improve the separation result by reducing the arity of the input relations of the queries to 3k + 1. (Some necessary background knowledge is given in the next section.)