A Transformational Decision Procedure for Non-Clausal Propositional Formulas

TL;DR

This paper introduces a novel decision procedure for propositional formulas that avoids branching by using validity-preserving transformations, optimizing variable selection and applying delta-set based enhancements for efficiency.

Contribution

It presents a non-branching, transformation-based decision procedure for propositional validity that improves efficiency through optimized variable selection and delta-set optimizations.

Findings

Procedure does not branch, reducing complexity.

Variable selection based on minimal formula size accelerates decision.

Delta-set optimizations enhance performance and formula reduction.

Abstract

A decision procedure for detecting valid propositional formulas is presented. It is based on the Davis-Putnam method and deals with propositional formulas that are initially converted to negational normal form. This procedure splits variables but, in contrast to other decision procedures based on the Davis-Putnam method, it does not branch. Instead, this procedure iteratively makes validity-preserving transformations of fragments of the formula. The transformations involve only a minimal formula part containing occurrences of the selected variable. Selection of the best variable for splitting is crucial in this decision procedure - it may shorten the decision process dramatically. A variable whose splitting leads to a minimal size of the transformed formula is selected. Also, the decision procedure performs plenty of optimizations based on calculation of delta-sets. Some optimizations lead to removing fragments of the formula. Others detect variables for which a single truth value assignment is sufficient. The latest information about this research can be found at http://www.sakharov.net/valid.html