Some parameters related to the computational complexity of partitioned list algorithms are evaluated. Specifically, an upper bound is computed for the average number of comparisons needed by the most unsophisticated version of a partitioned list algorithm for processing a Boolean function in v variables and u canonical clauses. For the same functions the average memory size required for processing is also computed. Furthermore the minimum memory size necessary for processing any Boolean function in u canonical clauses by either a partitioned or a nonpartitioned list algorithm is computed. Results obtained from the above comparisons demonstrate that partitioned list algorithms compare favorably with nonpartitioned ones both with regard to the time and the memory required for computation.

A common recursive formulation is presented for determining: 1) all the prime implicants, and 2) an irredundant normal form of any completely or incompletely specified Boolean function given in canonical form. Formulas for specific operators Pi and lrr2 solving these problems are given and recursive partitioned list algorithms are described for them. The solution of both of the above problems through recursive partitioned list algorithms is significantly faster than through the corresponding nonrecursive algorithms.

The structure of the algorithms implementing Quine's method for prime implicant determination is analyzed, and a new class of algorithms-partitioned list algorithms-for Quine's method is derived. Such algorithms are of particular interest for actual computation because they permit 1) avoiding repetitions while generating clauses, 2) representing each clause by only one binary configuration, 3) reducing memory capacity requirements, and 4) applying the basic operations by means of nonexhaustive techniques.