MINCE: A Static Global Variable-Ordering for SAT and BDD

Many popular algorithms that work with Boolean functions are dramatically dependent on the order of variables in input representations of Boolean functions. Such algorithms include satisfiability (SAT) solvers that are critical in formal verification and Binary Decision Diagrams (BDDs) manipulation algorithms that are increasingly popular in synthesis and verification. Finding better variable-orderings is a well-recognized problem in each of those contexts. Currently, all leading-edge variable-ordering algorithms are dynamic in the sense that they are invoked many times in the course of the “host” algorithm that solves SAT or manipulates BDDs. Examples include the DLIS ordering for SAT solvers and variable-sifting during BDD manipulations. In this work we propose a universal variable ordering MINCE (MIN Cut Etc.) that preprocesses a given Boolean formula in CNF. MINCE is completely independent from target algorithms and outperforms both DLIS for SAT and variable sifting for BDDs. We argue that MINCE tends to capture structural properties of Boolean functions arising from real-world applications.