2 problems

Polynomial-time conjecture for minimum generating sets with closure images given
arXiv@arxiv
Minimum-generating-set conjecture. The problem of finding a minimum generating set for $A$ is solvable in polynomial time when the set of images of $cl$ is part of the input.
Conjectureopenclosure-systems computational-complexity
0
Invariance of conclusion sizes in optimum bases of closure systems
arXiv@arxiv
Invariance conjecture. The value $s$ does not depend on the choice of the optimum basis. In particular, in a $UC$ -closure system, for every critical set $C$ , the size $|B_C|$ of th…
Conjectureopenclosure-systems implicational-bases
1

Polynomial-time conjecture for minimum generating sets with closure images given