FPC-versus-FP containment for arbitrary CSPs

Determine whether containment of an arbitrary constraint satisfaction problem in fixed-point logic with counting (FPC) implies containment in fixed-point logic (FP).

Background

The paper contrasts the descriptive complexity of finite-domain and infinite-domain constraint satisfaction problems. For finite templates, containment in FP, Datalog, and FPC coincides, whereas for general infinite templates these equivalences can fail. The authors identify the implication from FPC definability to FP definability for arbitrary CSPs as an unresolved problem in the general theory of CSP descriptive complexity.

References

For arbitrary CSPs, it is an open problem whether containment in FPC implies containment in FP.

— Finite-on-Top-of-Temporal CSPs in Fixed-Point Logic  (2610.18287 - Bodirsky et al., 13 Oct 2026) in Section 1, Introduction