Polynomial-time algorithms for generation of prime implicants

AbstractA notion of a neighborhood cube of a term of a Boolean function represented in the canonical disjunctive normal form is introduced. A relation between neighborhood cubes and prime implicants of a Boolean function is established. Various aspects of the problem of prime implicants generation are identified and neighborhood cube-based algorithms for their solution are developed. The correctness of algorithms is proven and their time complexity is analyzed. It is shown that all presented algorithms are polynomial in the number of minterms occurring in the canonical disjunctive normal form representation of a Boolean function. A summary of the known approaches to the solution of the problem of the generation of prime implicants is also included

Computer Aided Minimization Procedure for Boolean Functions

The paper describes CAMP, a Computer Aided Minimization Procedure for Boolean functions. The procedure is based on theorems of switching theory and fully exploits the power of degree of adjacency. The program does not generate any superfluous prime implicant and all the essential and elective prime implicants are chosen with no or minimum iteration. For shallow functions consisting mainly of essential prime implicants (EPIs) and a few selective prime implicants (SPIs), CAMP produces the exact minimal sum of product form. For dense functions consisting of a large number of inter-connected cyclic SPI chains, the solution may not be exactly minimal, but near minimal