110 research outputs found
DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL
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
Evaluating QBF Solvers: Quantifier Alternations Matter
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.Comment: preprint of a paper to be published at CP 2018, LNCS, Springer,
including appendi
On QBF Proofs and Preprocessing
QBFs (quantified boolean formulas), which are a superset of propositional
formulas, provide a canonical representation for PSPACE problems. To overcome
the inherent complexity of QBF, significant effort has been invested in
developing QBF solvers as well as the underlying proof systems. At the same
time, formula preprocessing is crucial for the application of QBF solvers. This
paper focuses on a missing link in currently-available technology: How to
obtain a certificate (e.g. proof) for a formula that had been preprocessed
before it was given to a solver? The paper targets a suite of commonly-used
preprocessing techniques and shows how to reconstruct certificates for them. On
the negative side, the paper discusses certain limitations of the
currently-used proof systems in the light of preprocessing. The presented
techniques were implemented and evaluated in the state-of-the-art QBF
preprocessor bloqqer.Comment: LPAR 201
Understanding and Extending Incremental Determinization for 2QBF
Incremental determinization is a recently proposed algorithm for solving
quantified Boolean formulas with one quantifier alternation. In this paper, we
formalize incremental determinization as a set of inference rules to help
understand the design space of similar algorithms. We then present additional
inference rules that extend incremental determinization in two ways. The first
extension integrates the popular CEGAR principle and the second extension
allows us to analyze different cases in isolation. The experimental evaluation
demonstrates that the extensions significantly improve the performance
QRAT+: Generalizing QRAT by a More Powerful QBF Redundancy Property
The QRAT (quantified resolution asymmetric tautology) proof system simulates
virtually all inference rules applied in state of the art quantified Boolean
formula (QBF) reasoning tools. It consists of rules to rewrite a QBF by adding
and deleting clauses and universal literals that have a certain redundancy
property. To check for this redundancy property in QRAT, propositional unit
propagation (UP) is applied to the quantifier free, i.e., propositional part of
the QBF. We generalize the redundancy property in the QRAT system by QBF
specific UP (QUP). QUP extends UP by the universal reduction operation to
eliminate universal literals from clauses. We apply QUP to an abstraction of
the QBF where certain universal quantifiers are converted into existential
ones. This way, we obtain a generalization of QRAT we call QRAT+. The
redundancy property in QRAT+ based on QUP is more powerful than the one in QRAT
based on UP. We report on proof theoretical improvements and experimental
results to illustrate the benefits of QRAT+ for QBF preprocessing.Comment: preprint of a paper to be published at IJCAR 2018, LNCS, Springer,
including appendi
SAT-Based Synthesis Methods for Safety Specs
Automatic synthesis of hardware components from declarative specifications is
an ambitious endeavor in computer aided design. Existing synthesis algorithms
are often implemented with Binary Decision Diagrams (BDDs), inheriting their
scalability limitations. Instead of BDDs, we propose several new methods to
synthesize finite-state systems from safety specifications using decision
procedures for the satisfiability of quantified and unquantified Boolean
formulas (SAT-, QBF- and EPR-solvers). The presented approaches are based on
computational learning, templates, or reduction to first-order logic. We also
present an efficient parallelization, and optimizations to utilize reachability
information and incremental solving. Finally, we compare all methods in an
extensive case study. Our new methods outperform BDDs and other existing work
on some classes of benchmarks, and our parallelization achieves a super-linear
speedup. This is an extended version of [5], featuring an additional appendix.Comment: Extended version of a paper at VMCAI'1
Incremental QBF Solving
We consider the problem of incrementally solving a sequence of quantified
Boolean formulae (QBF). Incremental solving aims at using information learned
from one formula in the process of solving the next formulae in the sequence.
Based on a general overview of the problem and related challenges, we present
an approach to incremental QBF solving which is application-independent and
hence applicable to QBF encodings of arbitrary problems. We implemented this
approach in our incremental search-based QBF solver DepQBF and report on
implementation details. Experimental results illustrate the potential benefits
of incremental solving in QBF-based workflows.Comment: revision (camera-ready, to appear in the proceedings of CP 2014,
LNCS, Springer
Dependency Schemes in QBF Calculi: Semantics and Soundness
We study the parametrisation of QBF resolution calculi by dependency schemes. One of the main problems in this area is to understand for which dependency schemes the resulting calculi are sound. Towards this end we propose a semantic framework for variable independence based on ‘exhibition’ by QBF models, and use it to express a property of dependency schemes called full exhibition that is known to be sufficient for soundness in Q-resolution. Introducing a generalised form of the long-distance resolution rule, we propose a complete parametrisation of classical long-distance Q-resolution, and show that full exhibition remains sufficient for soundness. We demonstrate that our approach applies to the current research frontiers by proving that the reflexive resolution path dependency scheme is fully exhibited
Shortening QBF Proofs with Dependency Schemes
We provide the first proof complexity results for QBF dependency calculi. By showing that the reflexive resolution path dependency scheme admits exponentially shorter Q-resolution proofs on a known family of instances, we answer a question first posed by Slivovsky and Szeider in 2014 [30]. Further, we conceive a method of QBF solving in which dependency recomputation is utilised as a form of inprocessing. Formalising this notion, we introduce a new calculus in which a dependency scheme is applied dynamically. We demonstrate the further potential of this approach beyond that of the existing static system with an exponential separation
Reinterpreting Dependency Schemes: Soundness Meets Incompleteness in DQBF
Dependency quantified Boolean formulas (DQBF) and QBF dependency schemes have been treated separately in the literature, even though both treatments extend QBF by replacing the linear order of the quantifier prefix with a partial order. We propose to merge the two, by reinterpreting a dependency scheme as a mapping from QBF into DQBF. Our approach offers a fresh insight on the nature of soundness in proof systems for QBF with dependency schemes, in which a natural property called ‘full exhibition’ is central. We apply our approach to QBF proof systems from two distinct paradigms, termed ‘universal reduction’ and ‘universal expansion’. We show that full exhibition is sufficient (but not necessary) for soundness in universal reduction systems for QBF with dependency schemes, whereas for expansion systems the same property characterises soundness exactly. We prove our results by investigating DQBF proof systems, and then employing our reinterpretation of dependency schemes. Finally, we show that the reflexive resolution path dependency scheme is fully exhibited, thereby proving a conjecture of Slivovsky
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