6 problems

Let $\mathcal{U}\mathcal{HIT}_{\!\delta=k}$ denote the class of unsatisfiable non-singular hitting clause-sets of deficiency $k$, where two different clauses clash in at least one…

Let $\mathcal{U}\mathcal{HIT}$ be the class of unsatisfiable hitting clause-sets, and let $\mathcal{U}\mathcal{HIT}_{\!\!\delta=k}$ denote those of deficiency $k$. Call a variable…

Linear Finiteness Conjecture. For $k\in\mathbb{N}$, $k\geq 2$,

Exact-variable Finiteness Conjecture. For every $k\in\mathbb{N}$,

Finiteness Conjecture. For every $k \in \mathbb{N}$, the number $n(F)$ of variables of an $F \in \Uclashns$ with $?=k$ is bounded.

Let $\mathcal{U}\mathcal{HIT}_{\!\delta=k}$ be the class of unsatisfiable hitting clause-sets of deficiency $k$. Let $\operatorname{singind}(F)$ denote the singular index of $F$, a…