Multi-source multi-target directed unreachability testing

Establish whether multi-digraph unreachability with multiple source vertices and multiple target vertices is constant query testable with one-sided error.

Background

The paper proves that multi-digraph unreachability with a single source and an arbitrary set of target vertices is constant query testable with one-sided error, using only completion queries of the form (a, *). The authors note that their reduction and the cited algorithm do not address multiple source vertices. Although this generalization is not needed for the paper’s main result on two-way regular path queries, its status remains unresolved.

References

We conjecture that it is possible to further generalize Theorem~\ref{thm:multidigraphproptest} to multi-digraph unreachability with multiple source (and target) vertices.

— Property Testing for Recursive Query Languages  (2609.03908 - Adler et al., 3 Sep 2026) in Section 2, immediately after Theorem 2.1

We conjecture that Theorem~\ref{thm:simple_branching} can be slightly generalized, e.g.\ to SBPs that admit reflexive loops and multi-edges.

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