Resolution and binary decision diagrams cannot simulate each other polynomially

There are many different ways of proving formulas in proposition logic. Many of these can easily be characterized as forms of resolution. Others use so-called binary decision diagrams (BDDs). Experimental evidence suggests that BDDs and resolution based techniques are fundamentally different, in the sense that their performance can differ very much on benchmarks. In this paper we confirm these findings by mathematical proof. We provide examples that are easy for BDDS and exponentially hard for any form of resolution, and vice versa, examples that ar easy for resolution and exponentially hard for BDDs

Resolution and binary decision diagrams cannot simulate each other polynomially

Proving formulas in propositional logic can be done in different ways. Some of these are based on of resolution, others on binary decision diagrams (BDDs). Experimental evidence suggests that BDDs and resolution based techniques are fundamentally different. This paper is an extended abstract of a paper [3] in which we confirm these findings by mathematical proof.We provide examples that are easy for BDDs and exponentially hard for any form of resolution, and vice versa, examples that are easy for resolution and exponentially hard for BDDs

Resolution and Binary Decision Diagrams Cannot Simulate Each Other Polynomially

There are many different ways of proving formulas in proposition logic. Many of these can easily be characterized as forms of resolution (e.g. [12] and [9]). Others use so-called binary decision diagrams (BDDs) [2, 10]. Experimental evidence suggests that BDDs and resolution based techniques are fundamentally different, in the sense that their performance can differ very much on benchmarks [14]. In this paper we confirm these findings by mathematical proof. We provide examples that are easy for BDDs and exponentially hard for any form of resolution, and vice versa, examples that are easy for resolution and exponentially hard for BDDs.

Generating Extended Resolution Proofs with a BDD-Based SAT Solver

In 2006, Biere, Jussila, and Sinz made the key observation that the underlying logic behind algorithms for constructing Reduced, Ordered Binary Decision Diagrams (BDDs) can be encoded as steps in a proof in the extended resolution logical framework. Through this, a BDD-based Boolean satisfiability (SAT) solver can generate a checkable proof of unsatisfiability for a set of clauses. Such a proof indicates that the formula is truly unsatisfiable without requiring the user to trust the BDD package or the SAT solver built on top of it. We extend their work to enable arbitrary existential quantification of the formula variables, a critical capability for BDD-based SAT solvers. We demonstrate the utility of this approach by applying a prototype solver to several problems that are very challenging for search-based SAT solvers, obtaining polynomially sized proofs on benchmarks for parity formulas, as well as the Urquhart, mutilated chessboard, and pigeonhole problems.Comment: Extended version of paper published at TACAS 202