This paper addresses the forbidden state problem of general marked graphs with uncontrollable transitions. The models need not to be safe nor cyclic. Control requirements are expressed as the conjunction of General Mutual Exclusion Constraints (GMEC) of markings of so-called critical places. Structural properties such as influence paths and influence zones are proposed to perform the worst-case analysis for each GMEC specification with any given initial marking when only uncontrollable transitions are allowed. Efficient solutions are proposed for the determination of the maximal uncontrollably reachable marking of any critical place, and this for many possible, more or less general, configurations of the net structure, even for the case of overlapping paths of critical places. Besides, we demonstrate that these results can be easily extended to unbounded nets and when critical places have negative weights. For the most general case, when analytical solution is not available, a linear programming approach is proposed. The great advantage of the proposed approach over existing methods is emphasized by using it to solve the supervisory control problem of the automated manufacturing system of AIP-RAO of Lyon, France (Atelier Inter-établissements de Productique Rhône Alpes Ouest).