Extended Resolution Proofs for Symbolic SAT Solving with Quantification

Abstract

Abstract. Symbolic SAT solving is an approach where the clauses of a CNF formula are represented using BDDs. These BDDs are then conjoined, and finally checking satisfiability is reduced to the question of whether the final BDD is identical to false. We present a method combining symbolic SAT solving with BDD quantification (variable elimination) and generation of extended resolution proofs. Proofs are fundamental to many applications, and our results allow the use of BDDs instead of-or in combination with-established proof generation techniques like clause learning. We have implemented a symbolic SAT solver with variable elimination that produces extended resolution proofs. We present details of our implementation, called EBDDRES, which is an extension of the system presented in [1], and also report on experimental results.

A First Step Towards a Unified Proof Checker for QBF

“…This behavior is probably due to the fact that the refutation files for Ebddres are so large, that merely saving them takes a lot of time. The same overhead is also observed in the propositional case [29,30]. For Quaffle the overhead is even higher, 1440%.…”

“…We have instrumented two other already existing solvers, (i) the BDD-based solver Ebddres [29,30] and (ii) the search-based solver Quaffle [12]. Ebddres produces both models and refutation traces whereas with Quaffle we are so far limited to refutation traces.…”

“…Then the logical operations of the solving algorithm are traced until it is shown that the Tseitin variable for the constant BDD zero has to be true, a contradiction. All the details except for universal quantification can be found in [29,30]. For universal quantification, the proof rule is as follows.…”

Compressing Propositional Refutations

“…Here we make a distinction between research on compression, i.e., shortening an already derived proof, and research on better decision procedures that find shorter proofs than earlier procedures [9].…”

DRAT-trim: Efficient Checking and Trimming Using Expressive Clausal Proofs

“…DRUP-trim, the predecessor to this tool, can produce a resolution graph of a proof in the TraceCheck [18,13,4] format. DRAT-trim can validate techniques that cannot be checked with resolution, and we designed a new format that is backward-compatible with TraceCheck, allowing expression of all presently-known solving techniques.…”