Red Spider Meets a Rainworm: Conjunctive Query Finite Determinacy Is Undecidable

We solve a well known and long-standing open problem in database theory, proving that Conjunctive Query Finite Determinacy Problem is undecidable. The technique we use builds on the top of the Red Spider method invented in our paper [GM15] to show undecidability of the same problem in the "unrestricted case" -- when database instances are allowed to be infinite. We also show a specific instance Q 0 , Q = \ Q 1 , Q 2 , ... Q k } such that the set Q of C Q s does not determine C Q Q 0 but finitely determines it. Finally, we claim that while Q 0 is finitely determined by Q , there is no FO-rewriting of Q 0 , with respect to Q