GMSNP-restricted RCSP tractability criterion

Determine whether, for every finite structure H and every structure R whose CSP is expressible in GMSNP, failure of (H,R) to rpp-construct the 3-colouring template implies that RCSP(H,R) is polynomial-time solvable.

Background

The paper proves a dichotomy for finite-domain RCSPs with GMSNP restrictions after replacing the restriction by its smallest finite factor. The authors leave open whether the direct rpp-construction criterion suffices without requiring the restriction itself to be finite.

The question concerns the interaction between GMSNP definability, finite-domain reductions, and the algebraic tractability boundary for restricted CSPs.