Evaluating QBF Solvers: Quantifier Alternations Matter

Lonsing, Florian; Egly, Uwe

doi:10.1007/978-3-319-98334-9_19

Cited by 25 publications

(17 citation statements)

References 45 publications

(73 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In almost all cases, the solver that handles ψ ∀ needs more time than the solver that handles ψ ∃ . This may be founded on the observation that many QBFs have considerably more existential variables than universal variables [36], hence the instantiations added to ψ ∀ are much larger than the instantiations added to ψ ∃ .…”

Section: Methodsmentioning

confidence: 99%

Expansion-Based QBF Solving Without Recursion

Bloem

Braud-Santoni

Hadzic

et al. 2018

2018 Formal Methods in Computer Aided Design (FMCAD)

Self Cite

View full text Add to dashboard Cite

In recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over Boolean variables. Such approaches partially expand one type of variable (either existential or universal) and pass the obtained formula to a SAT solver for deciding the QBF. State-of-the-art expansionbased solvers process the given formula quantifier-block wise and recursively apply expansion until a solution is found.In this paper, we present a novel algorithm for expansionbased QBF solving that deals with the whole quantifier prefix at once. Hence recursive applications of the expansion principle are avoided. Experiments indicate that the performance of our simple approach is comparable with the state of the art of QBF solving, especially in combination with other solving techniques.

show abstract

Section: Methodsmentioning

confidence: 99%

Expansion-Based QBF Solving Without Recursion

Bloem

Braud-Santoni

Hadzic

et al. 2018

2018 Formal Methods in Computer Aided Design (FMCAD)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Further, we considered the 402 PCNFs in their original form and preprocessed by Bloqqer and partitioned them into subsets containing PCNFs with at most two and with three or more quantifier alternations. Such partitioning is motivated by a related experimental study [30] where a large diversity of solver performance was observed on instance classes defined by alternations. Tables 2 and 3 show solver performance on these subsets without and with preprocessing, respectively.…”

Section: Methodsmentioning

confidence: 99%

DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL

Lonsing

Egly

2017

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

We present the latest major release version 6.0 of the quantified Boolean formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of the conflict-driven clause learning (CDCL) paradigm implemented in state of the art propositional satisfiability (SAT) solvers. The Q-resolution calculus (QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0 implements a variant of QCDCL which is based on a generalization of QRES. This generalization is due to a set of additional axioms and leaves the original Q-resolution rules unchanged. The generalization of QRES enables QCDCL to potentially produce exponentially shorter proofs than the traditional variant. We present an overview of the features implemented in DepQBF and report on experimental results which demonstrate the effectiveness of generalized QRES in QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS, Springer, 201

show abstract

“…Generally speaking, expansion/abstraction solvers tend to do better on instances with few alternations, whereas QCDCL solvers are at an advantage on instances with many alternations. Standard benchmark sets contain many instances with only a single alternation (Lonsing & Egly, 2018), presumably because many problems of interest can be encoded in such formulas. Figure 3 shows the number of solved prenex non-CNF instances broken down by the number of quantifier alternations.…”

Section: Decision Heuristic Restart Strategy and Constraint Deletion Policymentioning

confidence: 99%

Dependency Learning for QBF

Peitl¹,

Slivovsky²,

Szeider³

2019

jair

View full text Add to dashboard Cite

Quantified Boolean Formulas (QBFs) can be used to succinctly encode problems from domains such as formal verification, planning, and synthesis. One of the main approaches to QBF solving is Quantified Conflict Driven Clause Learning (QCDCL). By default, QCDCL assigns variables in the order of their appearance in the quantifier prefix so as to account for dependencies among variables. Dependency schemes can be used to relax this restriction and exploit independence among variables in certain cases, but only at the cost of nontrivial interferences with the proof system underlying QCDCL. We introduce dependency learning, a new technique for exploiting variable independence within QCDCL that allows solvers to learn variable dependencies on the fly. The resulting version of QCDCL enjoys improved propagation and increased flexibility in choosing variables for branching while retaining ordinary (long-distance) Q-resolution as its underlying proof system. We show that dependency learning can achieve exponential speedups over ordinary QCDCL. Experiments on standard benchmark sets demonstrate the effectiveness of this technique.

show abstract

Evaluating QBF Solvers: Quantifier Alternations Matter

Cited by 25 publications

References 45 publications

Expansion-Based QBF Solving Without Recursion

Expansion-Based QBF Solving Without Recursion

DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL

Dependency Learning for QBF

Contact Info

Product

Resources

About