# Solving QBF by Abstraction

@inproceedings{HeckingHarbusch2018SolvingQB, title={Solving QBF by Abstraction}, author={Jesko Hecking-Harbusch and Leander Tentrup}, booktitle={GandALF}, year={2018} }

Many verification and synthesis approaches rely on solving techniques for quantified Boolean formulas (QBF). Consequently, solution witnesses, in the form of Boolean functions, become more and more important as they represent implementations or counterexamples. We present a recursive counterexample guided abstraction and refinement algorithm (CEGAR) for solving and certifying QBFs that exploits structural reasoning on the formula level. The algorithm decomposes the given QBF into one…

## 17 Citations

CAQE and QuAbS: Abstraction Based QBF Solvers

- Computer ScienceJ. Satisf. Boolean Model. Comput.
- 2019

The clausal abstraction algorithm started as a solving algorithm for QBFs in prenex conjunctive normal form incorporating an efficient Skolem and Herbrand function extraction and was extended to non-prenex and negation normal form formulas, leading the way for improved performance in solving and function extraction.

Clausal Abstraction for DQBF

- Computer ScienceSAT
- 2019

The clausal abstraction algorithm for quantified Boolean formulas (QBF) is lifted to DQBF, a logic admitting existential quantification over Boolean functions, which allows for elegantly state synthesis problems in verification such as the search for invariants, programs, or winning regions of games.

Clausal Abstraction for DQBF (full version)

- Computer Science
- 2018

The clausal abstraction algorithm for quantified Boolean formulas (QBF) is lifted to DQBF, and the implementation dCAQE solves significantly more formulas than the existing DQ BF algorithms.

Non-prenex QBF Solving Using Abstraction

- Computer ScienceSAT
- 2016

A modified algorithm is presented that lifts the restriction on prenex quantifiers and handles tree-shaped quantifier hierarchies where different branches can be solved independently and exploits this property by solving independent branches in parallel.

Parallel Solving of Quantified Boolean Formulas

- Computer ScienceHandbook of Parallel Constraint Reasoning
- 2018

This chapter reviews and compares approaches for solving QBFs in parallel and concludes that QBFs provide an attractive framework for encoding many applications from verification, artificial intelligence, and synthesis, thus motivating the quest for efficient solving technology.

A Cube Distribution Approach to QBF Solving and Certificate Minimization

- Computer ScienceCP
- 2019

A new view on QBF solving and certificate generation is given by the cube distribution interpretation, which provides a largely increased flexibility for QBF reasoning and allows compact certificate derivation with don’t cares.

Encodings of Bounded Synthesis

- Computer ScienceTACAS
- 2017

This paper considers different reductions of the bounded synthesis problem of linear-time temporal logic to constraint systems given as Boolean formulas (SAT), quantified boolean formulas (QBF), and dependency quantifiedolean formulas (DQBF).

Bounded Model Checking for Hyperproperties

- Computer ScienceTACAS
- 2021

This paper introduces a bounded model checking (BMC) algorithm for hyperproperties expressed in HyperLTL, which — to the best of our knowledge — is the first such algorithm. Just as the classic BMC…

HyperQube: A QBF-Based Bounded Model Checker for Hyperproperties

- Computer ScienceArXiv
- 2021

This paper presents HyperQube, a push-button QBF-based bounded model checker for hyperproperties, which takes as input a NuSMV model and a formula expressed in the temporal logic HyperLTL to seamlessly deal with quantifier alternations.

Symbolic vs. Bounded Synthesis for Petri Games

- Computer ScienceSYNT@CAV
- 2017

Bounded synthesis is compared to the existing implementation of the symbolic approach in the synthesis tool ADAM, and experimental results on a collection of benchmarks are presented, including one new benchmark family, modeling manufacturing and workflow scenarios with multiple concurrent processes.

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