4 problems

A hitting formula is a set of Boolean clauses such that no two clauses can be simultaneously falsified. A hitting formula is unsatisfiable when no Boolean assignment satisfies all…

Bounded-hermitian-rank satisfiability conjecture. Satisfiability decision for generalised clause-sets can be done in polynomial time for bounded hermitian rank.

Multihitting satisfiability conjecture. Satisfiability decision for multihitting generalised clause-sets can be done in polynomial time.

Kullmann's conjecture. In fact, all classes $mathcal{Mhspace{0.8pt}U}(k)$ are in $operatorname{P}$ for fixed $k$.