HQSpre – An Effective Preprocessor for QBF and DQBF

We present an experimental study of the effects of quantifier alternations on the evaluation of quantified Boolean formula (QBF) solvers. The number of quantifier alternations in a QBF in prenex conjunctive normal form (PCNF) is directly related to the theoretical hardness of the respective QBF satisfiability problem in the polynomial hierarchy. We show empirically that the performance of solvers based on different solving paradigms substantially varies depending on the numbers of alternations in PCNFs. In related theoretical work, quantifier alternations have become the focus of understanding the strengths and weaknesses of various QBF proof systems implemented in solvers. Our results motivate the development of methods to evaluate orthogonal solving paradigms by taking quantifier alternations into account. This is necessary to showcase the broad range of existing QBF solving paradigms for practical QBF applications. Moreover, we highlight the potential of combining different approaches and QBF proof systems in solvers.

Section: Resultssupporting

confidence: 75%

Evaluating QBF Solvers: Quantifier Alternations Matter

Lonsing

Egly

2018

“…QRATPre+ improves on state-of-the-art preprocessors and solvers in terms of formula size reduction and solved instances. We ran experiments with the preprocessors Bloqqer v37 [6] and HQSpre 1.3 [25], and the solvers CAQE (commit-ID 9b95754 on GitHub) [22,23], RAReQS 1.1 [10], Ijtihad v2 [2], Qute 1.1 [21], and DepQBF 6.03 [16]. The solvers implement different solving paradigms, e.g., QCDCL (Qute and DepQBF), expansion (RAReQS and Ijtihad), and clausal abstraction (CAQE).…”

Section: Methodsmentioning

confidence: 99%

QRATPre+: Effective QBF Preprocessing via Strong Redundancy Properties

Lonsing

Egly

2019

We present version 2.0 of QRATPre+, a preprocessor for quantified Boolean formulas (QBFs) based on the QRAT proof system and its generalization QRAT + . These systems rely on strong redundancy properties of clauses and universal literals. QRATPre+ is the first implementation of these redundancy properties in QRAT and QRAT + used to simplify QBFs in preprocessing. It is written in C and features an API for easy integration in other QBF tools. We present implementation details and report on experimental results demonstrating that QRATPre+ improves upon the power of state-of-the-art preprocessors and solvers.

“…Bounded unsatisfiability [7] asserts the existence of a partial (bounded) expansion tree that guarantees that no Skolem function exists. QBF preprocessing techniques have been lifted to DQBF [26,27]. Our solving technique is based on clausal abstraction [23] (also called clause selection [17]) for QBF, which can provide certificates [23].…”

Section: Related Workmentioning

confidence: 99%

Clausal Abstraction for DQBF

Tentrup

Rabe

2019

Dependency quantified Boolean formulas (DQBF) is a logic admitting existential quantification over Boolean functions, which allows us to elegantly state synthesis problems in verification such as the search for invariants, programs, or winning regions of games. In this paper, we lift the clausal abstraction algorithm for quantified Boolean formulas (QBF) to DQBF. Clausal abstraction for QBF is an abstraction refinement algorithm that operates on a sequence of abstractions that represent the different quantifier levels. For DQBF we need to generalize this principle to partial orders of abstractions. The two challenges to overcome are: (1) Clauses may contain literals with incomparable dependencies, which we address by the recently proposed proof rule called Fork Extension, and (2) existential variables may have spurious dependencies, which we prevent by tracking consistency requirements during the execution. Our implementation dCAQE solves significantly more formulas than the existing DQBF algorithms.