When a molecule is exposed to a laser field which leads to dissociation, all field-free vibrational bound states become resonances, with complex eigenenergies described by non Hermitian quantum mechanics. It is possible to produce the coalescence of pairs of such eigenenergies, with appropriate choices of laser frequency and intensity, these particular values defining an exceptional point. We review some of the aspects of this very special situation. There are two principal characteristics of the adiabatic dynamics of a pair of vibrational states when the laser pulse encloses their exceptional point: the complete population inversion and the different type of transient resonance states. According to clock or anticlockwise loops in the frequency-intensity plane, the resonances can either be of Shape or Feshbach-type. This leads to a variety of different responses according to the initial state of the molecule that can be used to build a finite state logic machine based on the exceptional points of molecular photodissociation. The molecule chosen for this study is Na2.