I was looking for the complexity class of computing MCS:Given a boolean formula $\mathcal{F = c_1 \wedge c_2,...,\wedge c_m}$ represented in CNF, a MCS is a subset of the set of clauses $\mathcal{C}$ such that $\mathcal{F} \backslash \mathcal{C} \in SAT$ but $\forall c \in \mathcal{C}, F \backslash(\mathcal{C}\backslash c) \in UNSAT$.My first question is to which complexity class does this problem belong?Second, what is the relation between this complexity class and $\sharp P-complete$ problems? i.e. does it make sense to use MCS in order to solve problem which is in sharp p complete?
Complexity class of MCS and relation to #p
cc.complexity theory;boolean functions;polynomial hierarchy;max2sat