Extension of strongly linear testing to unrestricted schemas

Establish whether falsity of every strongly linear monadic Datalog program remains constant query testable with one-sided error when the underlying schema is unrestricted rather than binary.

Background

The paper proves constant-query testability for falsity of strongly linear monadic Datalog programs over binary schemas by reducing them to two-way regular path queries. The authors explicitly conjecture that the same result should hold for unrestricted schemas, but do not establish this extension.

References

We conjecture, however, that the main result of this section also holds for unrestricted schemas.

— Property Testing for Recursive Query Languages  (2609.03908 - Adler et al., 3 Sep 2026) in Section 4.1, immediately before Theorem 4.2

We do not know, by contrast, how to deal with other seemingly harmless extensions. For instance, this is the case for replacing the $R_i$ and $T_j$ edges with paths of constant length and for dropping the distinctness of the relation symbols.

— Property Testing for Recursive Query Languages  (2609.03908 - Adler et al., 3 Sep 2026) in Section 4.2, immediately after Theorem 4.4

While we establish the lower bound part of the question for self-join free programs, a corresponding upper bound remains wide open.

— Property Testing for Recursive Query Languages  (2609.03908 - Adler et al., 3 Sep 2026) in Section 4, paragraph immediately before Section 4.1