Computing prime implicates by pruning the search space and accelerating subsumption

The prime implicate trie (pi-trie) of a logical formula is a tree whose branches are labeled with the prime implicates of the formula. An algorithm that builds the pi-trie from a logical formula was introduced in [12]; it builds the trie recursively and makes extensive use of subsumption testing. A more efficient version in which the use of subsumption is reduced is presented in this paper. The improved algorithm is illustrated with experiments. The algorithm naturally lends itself to selecting restricted sets — for example, only positive prime implicates or only those of bounded length, both useful properties for some applications. Such restrictions can provide significant advantages in efficiency since the set of all prime implicates of a logical formula is typically exponential in size.