Extended Resolution Proofs for Conjoining BDDs

Sinz, Carsten; Biere, Armin

doi:10.1007/11753728_60

Cited by 48 publications

(68 citation statements)

References 36 publications

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“…Recently, there has been a lot of interest in the relative efficiency of satisfiability checking methods based on resolution and OBDDs [1,2,3,4,5,6]. While OBBDs in general are known to be in cases exponentially more efficient that unrestricted resolution [7], it has been recently shown [6] that the restricted OBDD aj proof system, consisting only of the rather weak Axiom and Join rules which correspond to the Apply OBDD operator (i.e., disallowing symbolic quantifier elimination and reordering), does not polynomially simulate unrestricted resolution.…”

Section: Introductionmentioning

confidence: 99%

On the Relative Efficiency of DPLL and OBDDs with Axiom and Join

Järvisalo

2011

Principles and Practice of Constraint Programming – CP 2011

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Abstract. This paper studies the relative efficiency of ordered binary decision diagrams (OBDDs) and the Davis-Putnam-Logemann-Loveland procedure (DPLL), two of the main approaches to solving Boolean satisfiability instances. Especially, we show that OBDDs, even when constructed using only the rather weak axiom and join rules, can be exponentially more efficient than DPLL or, equivalently, tree-like resolution. Additionally, by strengthening via simple arguments a recent result-stating that such OBDDs do not polynomially simulate unrestricted resolution-we also show that the opposite holds: there are cases in which DPLL is exponentially more efficient out of the two considered systems. Hence DPLL and OBDDs constructed using only the axiom and join rules are polynomially incomparable. This further highlights differences between search-based and compilation-based approaches to Boolean satisfiability.

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Section: Introductionmentioning

confidence: 99%

On the Relative Efficiency of DPLL and OBDDs with Axiom and Join

Järvisalo

2011

Principles and Practice of Constraint Programming – CP 2011

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“…Sinz and Biere [6] and later Biere [1] describe and discuss a system of proof traces and checking for Sat solvers based on conflict-driven clause learning, such as zchaff, minisat, picosat, and many others. In many respects, their proposal is simply the union of two earlier ground-breaking proposals: Goldberg and Novikov proposed to output the literals of each derived conflict clause [4], while Zhang and Malik proposed to output the sequence of clause numbers whose linear resolution would create each derived conflict clause [9].…”

Section: Introductionmentioning

confidence: 99%

Improved Conflict-Clause Minimization Leads to Improved Propositional Proof Traces

Gelder

2009

Lecture Notes in Computer Science

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Abstract. Recent empirical results show that recursive, or expensive, conflict-clause minimization is quite beneficial on industrial-style propositional satisfiability problems. The details of this procedure appear to be unpublished to date, but may be found in the open-source code of MiniSat 2.0, for example. Biere reports that proof traces are made more complicated when conflict-clause minimization is used because some clauses need to be resolved upon multiple times during the minimization procedure as found in MiniSat 2.0. Biere proposes a proof-trace format in which the set of clause numbers needed for a certain derivation is given, but their order is not specified. This paper presents a new procedure for conflict-clause minimization that is slightly more efficient and, more importantly, discovers a correct order so that each clause used for the derivation is resolved upon only once. This permits the proof trace to specify the order in which to use the clauses, greatly reducing the burden on software that processes the proof trace. The method is validated on the unsatisfiable formulas used for industrial benchmarks in the verifiedunsatisfiable track of the SAT 2007 competition.

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“…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.…”

Section: Methodsmentioning

confidence: 99%

“…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.…”

Section: Methodsmentioning

confidence: 99%

A First Step Towards a Unified Proof Checker for QBF

Jussila

Biere

Sinz

et al.

Theory and Applications of Satisfiability Testing – SAT 2007

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Abstract. Compared to SAT, there is no simple concept of what a solution to a QBF problem is. Furthermore, as the series of QBF evaluations shows, the QBF solvers that are available often disagree. Thus, proof generation for QBF seems to be even more important than for SAT. In this paper we propose a new uniform proof format, which captures refutations and witnesses for a variety of QBF solvers, and is based on a novel extended resolution rule for QBF. Our experiments show the flexibility of this new format. We also identify shortcomings of our format and conjecture that a purely resolution based proof calculus is not powerful enough to trace the most efficient solvers.

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Extended Resolution Proofs for Conjoining BDDs

Cited by 48 publications

References 36 publications

On the Relative Efficiency of DPLL and OBDDs with Axiom and Join

On the Relative Efficiency of DPLL and OBDDs with Axiom and Join

Improved Conflict-Clause Minimization Leads to Improved Propositional Proof Traces

A First Step Towards a Unified Proof Checker for QBF

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