Disjunctive and conjunctive normal forms of pseudo-Boolean functions

Stephan Foldes, Peter L. Hammer
2000 Discrete Applied Mathematics  
After showing that every pseudo-Boolean function (i.e. real-valued function with binary variables) can be represented by a disjunctive normal form (essentially the maximum of several weighted monomials), the concepts of implicants and of prime implicants are analyzed in the pseudo-Boolean context, and a consensus-type method is presented for ÿnding all the prime implicants of a pseudo-Boolean function. In a similar way the concepts of conjunctive normal form, implicates and prime implicates, as
more » ... well as the resolution method are examined in the case of pseudo-Boolean functions. ?
doi:10.1016/s0166-218x(00)00276-6 fatcat:e4wd2a6bcbbdjp6arbtfcihxpi