On the relationship between parsimonious covering and Boolean minimization

The authors explain some of the relationships of the Boolean minimization problem (BMP) to a formalization of abductive inference called parsimonious covering (PC). Abductive inference often occurs in diagnostic problems such as finding the causes of circuit faults or determining the disease causing the symptoms reported by a patient. Parsimonious covering involves covering all observed facts by means of a parsimonious set of explanations that can account for the observation. It is shown that only the prime implicants of a given Boolean function in a BMP, rather than any general product terms, are considered analogous to disorders in a PC problem