Given a Boolean formula in disjunctive normal form, the variable delet
ion control set problem consists in finding a minimum cardinality set
of variables whose deletion from the formula results in a DNF satisfyi
ng some prescribed property. Similar problems can be defined with resp
ect to the fixation of variables or the deletion of terms in a DNF. In
this paper, we investigate the complexity of such problems for a broa
d class of DNF properties.