Trie Based Subsumption and Improving the pi-Trie Algorithm

Abstract

An algorithm that stores the prime implicates of a propositional logical formula in a trie was developed in [10]. In this paper, an improved version of that pi-trie algorithm is presented. It achieves its speedup primarily by significantly decreasing subsumption testing. Preliminary experiments indicate the new algorithm to be substantially faster and the trie based subsumption tests to be considerably more efficient than the clause by clause approach originally employed.

Techniques and Tools for Trustworthy Composition of Pre-Designed Embedded Software Components

“…In [34], a branch-by-branch analysis leads to the algorithm introduced there. In [35], a set oriented characterization is not only more intuitive but leads to a more efficient version of the algorithm. The added efficiency stems from three improvements.…”

“…The difference in performance of the newer algorithm over the original is quite dramatic: Figure 15 compares (in log scale) the pi-trie algorithm from [34] to the updated version in [35], using the recursive, trie-based and operators. The input for both algorithms is a 15-variable 3-CNF with varying numbers of clauses and the runtimes averaged over 20 trials.…”

“…In synthesis of polychronus systems, prime implicates that are positive, containing only positive literals, and short, especially unit prime implicates, are of special interest. Such prime implicates can always be selected from the entire set of prime implicates, but generating only the prime implicates of interest is not only preferable, but much more efficient [35,36]. Figure 16 has the results of an experiment with a 13-variable 3-CNF formula.…”