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Florian Lonsing

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19 papers

2 author rows

FM Conference 2026 Conference Paper

Pono 2. 0: A Versatile SMT-Based Model Checker for Safety and Liveness (Long Tool Paper)

Áron Ricardo Perez-Lopez
Po-Chun Chien
Florian Lonsing
Samantha Archer
Ahmed Irfan
Clark Barrett

Abstract We introduce an updated version of the Pono model checker. Pono is a versatile SMT-based model checker that integrates multiple verification algorithms and interfaces with a wide range of SMT solvers through a solver-agnostic back end. It emphasizes usability, offering support for commonly used input formats and providing C++ and Python APIs for programmatic access. The new version 2. 0 introduces several important new features, including support for liveness properties, new interpolation-based safety-checking engines, a new VMT-LIB front end, and a number of usability and performance enhancements. An evaluation of the new version demonstrates significant improvements in performance over its previous version and comparable performance to other state-of-the-art model checkers. These results highlight Pono 2. 0’s effectiveness as a general-purpose and easily extensible verification platform.

SAT Conference 2019 Conference Paper

QRATPre+: Effective QBF Preprocessing via Strong Redundancy Properties

Florian Lonsing
Uwe Egly

Abstract We present version 2. 0 of QRATPre +, a preprocessor for quantified Boolean formulas (QBFs) based on the \(\mathsf {QRAT} \) proof system and its generalization \(\mathsf {QRAT}^{+} \). These systems rely on strong redundancy properties of clauses and universal literals. QRATPre + is the first implementation of these redundancy properties in \(\mathsf {QRAT} \) and \(\mathsf {QRAT}^{+} \) 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.

SAT Conference 2016 Conference Paper

HordeQBF: A Modular and Massively Parallel QBF Solver

Tomás Balyo
Florian Lonsing

Abstract The recently developed massively parallel satisfiability (SAT) solver HordeSAT was designed in a modular way to allow the integration of any sequential CDCL-based SAT solver in its core. We integrated the QCDCL-based quantified Boolean formula (QBF) solver DepQBF in HordeSAT to obtain a massively parallel QBF solver—HordeQBF. In this paper we describe the details of this integration and report on results of the experimental evaluation of HordeQBF’s performance. HordeQBF achieves superlinear average and median speedup on the hard application instances of the 2014 QBF Gallery.

SAT Conference 2016 Conference Paper

Q-Resolution with Generalized Axioms

Florian Lonsing
Uwe Egly
Martina Seidl

Abstract Q-resolution is a proof system for quantified Boolean formulas (QBFs) in prenex conjunctive normal form (PCNF) which underlies search-based QBF solvers with clause and cube learning (QCDCL). With the aim to derive and learn stronger clauses and cubes earlier in the search, we generalize the axioms of the Q-resolution calculus resulting in an exponentially more powerful proof system. The generalized axioms introduce an interface of Q-resolution to any other QBF proof system allowing for the direct combination of orthogonal solving techniques. We implemented a variant of the Q-resolution calculus with generalized axioms in the QBF solver DepQBF. As two case studies, we apply integrated SAT solving and resource-bounded QBF preprocessing during the search to heuristically detect potential axiom applications. Experiments with application benchmarks indicate a substantial performance improvement.

AIJ Journal 2016 Journal Article

The QBF Gallery: Behind the scenes

Florian Lonsing
Martina Seidl
Allen Van Gelder

Over the last few years, much progress has been made in the theory and practice of solving quantified Boolean formulas (QBF). Novel solvers have been presented that either successfully enhance established techniques or implement novel solving paradigms. Powerful preprocessors have been realized that tune the encoding of a formula to make it easier to solve. Frameworks for certification and solution extraction emerged that allow for a detailed interpretation of a QBF solver's results, and new types of QBF encodings were presented for various application problems. To capture these developments the QBF Gallery was established in 2013. The QBF Gallery aims at providing a forum to assess QBF tools and to collect new, expressive benchmarks that allow for documenting the status quo and that indicate promising research directions. These benchmarks became the basis for the experiments conducted in the context of the QBF Gallery 2013 and follow-up evaluations. In this paper, we report on the setup of the QBF Gallery. To this end, we conducted numerous experiments which allowed us not only to assess the quality of the tools, but also the quality of the benchmarks.

LPAR Conference 2015 Conference Paper

Automated Benchmarking of Incremental SAT and QBF Solvers

Uwe Egly
Florian Lonsing
Johannes Oetsch

Abstract Incremental SAT and QBF solving potentially yields improvements when sequences of related formulas are solved. An incremental application is usually tailored towards some specific solver and decomposes a problem into incremental solver calls. This hinders the independent comparison of different solvers, particularly when the application program is not available. As a remedy, we present an approach to automated benchmarking of incremental SAT and QBF solvers. Given a collection of formulas in (Q)DIMACS format generated incrementally by an application program, our approach automatically translates the formulas into instructions to import and solve a formula by an incremental SAT/QBF solver. The result of the translation is a program which replays the incremental solver calls and thus allows to evaluate incremental solvers independently from the application program. We illustrate our approach by different hardware verification problems for SAT and QBF solvers.

JAIR Journal 2015 Journal Article

Clause Elimination for SAT and QSAT

Marijn Heule
Matti Järvisalo
Florian Lonsing
Martina Seidl
Armin Biere

The famous archetypical NP-complete problem of Boolean satisfiability (SAT) and its PSPACE-complete generalization of quantified Boolean satisfiability (QSAT) have become central declarative programming paradigms through which real-world instances of various computationally hard problems can be efficiently solved. This success has been achieved through several breakthroughs in practical implementations of decision procedures for SAT and QSAT, that is, in SAT and QSAT solvers. Here, simplification techniques for conjunctive normal form (CNF) for SAT and for prenex conjunctive normal form (PCNF) for QSAT---the standard input formats of SAT and QSAT solvers---have recently proven very effective in increasing solver efficiency when applied before (i.e., in preprocessing) or during (i.e., in inprocessing) satisfiability search. In this article, we develop and analyze clause elimination procedures for pre- and inprocessing. Clause elimination procedures form a family of (P)CNF formula simplification techniques which remove clauses that have specific (in practice polynomial-time) redundancy properties while maintaining the satisfiability status of the formulas. Extending known procedures such as tautology, subsumption, and blocked clause elimination, we introduce novel elimination procedures based on asymmetric variants of these techniques, and also develop a novel family of so-called covered clause elimination procedures, as well as natural liftings of the CNF-level procedures to PCNF. We analyze the considered clause elimination procedures from various perspectives. Furthermore, for the variants not preserving logical equivalence under clause elimination, we show how to reconstruct solutions to original CNFs from satisfying assignments to simplified CNFs, which is important for practical applications for the procedures. Complementing the more theoretical analysis, we present results on an empirical evaluation on the practical importance of the clause elimination procedures in terms of the effect on solver runtimes on standard real-world application benchmarks. It turns out that the importance of applying the clause elimination procedures developed in this work is empirically emphasized in the context of state-of-the-art QSAT solving.

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LPAR Conference 2015 Conference Paper

Enhancing Search-Based QBF Solving by Dynamic Blocked Clause Elimination

Florian Lonsing
Fahiem Bacchus
Armin Biere
Uwe Egly
Martina Seidl

Abstract Among preprocessing techniques for quantified Boolean formula (QBF) solving, quantified blocked clause elimination (QBCE) has been found to be extremely effective. We investigate the power of dynamically applying QBCE in search-based QBF solving with clause and cube learning (QCDCL). This dynamic application of QBCE is in sharp contrast to its typical use as a mere preprocessing technique. In our dynamic approach, QBCE is applied eagerly to the formula interpreted under the assignments that have been enumerated in QCDCL. The tight integration of QBCE in QCDCL results in a variant of cube learning which is exponentially stronger than the traditional method. We implemented our approach in the QBF solver DepQBF and ran experiments on instances from the QBF Gallery 2014. On application benchmarks, QCDCL with dynamic QBCE substantially outperforms traditional QCDCL. Moreover, our approach is compatible with incremental solving and can be combined with preprocessing techniques other than QBCE.

SAT Conference 2015 Conference Paper

Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API

Florian Lonsing
Uwe Egly

Abstract We consider the incremental computation of minimal unsatisfiable cores (MUCs) of QBFs. To this end, we equipped our incremental QBF solver DepQBF with a novel API to allow for incremental solving based on clause groups. A clause group is a set of clauses which is incrementally added to or removed from a previously solved QBF. Our implementation of the novel API is related to incremental SAT solving based on selector variables and assumptions. However, the API entirely hides selector variables and assumptions from the user, which facilitates the integration of DepQBF in other tools. We present implementation details and, for the first time, report on experiments related to the computation of MUCs of QBFs using DepQBF’s novel clause group API.

SAT Conference 2014 Conference Paper

MPIDepQBF: Towards Parallel QBF Solving without Knowledge Sharing

Charles Jordan
Lukasz Kaiser
Florian Lonsing
Martina Seidl

Abstract Inspired by recent work on parallel SAT solving, we present a lightweight approach for solving quantified Boolean formulas (QBFs) in parallel. In particular, our approach uses a sequential state-of-the-art QBF solver to evaluate subformulas in working processes. It abstains from globally exchanging information between the workers, but keeps learnt information only locally. To this end, we equipped the state-of-the-art QBF solver DepQBF with assumption-based reasoning and integrated it in our novel solver MPIDepQBF as backend solver. Extensive experiments on standard computers as well as on the supercomputer Tsubame show the impact of our approach.

SAT Conference 2013 Conference Paper

Efficient Clause Learning for Quantified Boolean Formulas via QBF Pseudo Unit Propagation

Florian Lonsing
Uwe Egly
Allen Van Gelder

Abstract Recent solvers for quantified boolean formulas (QBF) use a clause learning method based on a procedure proposed by Giunchiglia et al. (JAIR 2006), which avoids creating tautological clauses. Recently, an exponential worst case for this procedure has been shown by Van Gelder (CP 2012). That paper introduced QBF Pseudo Unit Propagation (QPUP) for non-tautological clause learning in a limited setting and showed that its worst case is theoretically polynomial, although it might be impractical in a high-performance QBF solver, due to excessive time and space consumption. No implementation was reported. We describe an enhanced version of QPUP learning that is practical to incorporate into high-performance QBF solvers, being compatible with pure-literal rules and dependency schemes. It can be used for proving in a concise format that a QBF formula is either unsatisfiable or satisfiable (working on both proofs in tandem). A lazy version of QPUP permits non-tautological clauses to be learned without actually carrying out resolutions, but this version is unable to produce proofs. Experimental results show that QPUP is somewhat faster than the previous non-tautological clause learning procedure on benchmarks from QBFEVAL-12-SR.

LPAR Conference 2013 Conference Paper

Long-Distance Resolution: Proof Generation and Strategy Extraction in Search-Based QBF Solving

Uwe Egly
Florian Lonsing
Magdalena Widl

Abstract Strategies (and certificates) for quantified Boolean formulas (QBFs) are of high practical relevance as they facilitate the verification of results returned by QBF solvers and the generation of solutions to problems formulated as QBFs. State of the art approaches to obtain strategies require traversing a Q-resolution proof of a QBF, which for many real-life instances is too large to handle. In this work, we consider the long-distance Q-resolution (LDQ) calculus, which allows particular tautological resolvents. We show that for a family of QBFs using the LDQ-resolution allows for exponentially shorter proofs compared to Q-resolution. We further show that an approach to strategy extraction originally presented for Q-resolution proofs can also be applied to LDQ-resolution proofs. As a practical application, we consider search-based QBF solvers which are able to learn tautological clauses based on resolution and the conflict-driven clause learning method. We prove that the resolution proofs produced by these solvers correspond to proofs in the LDQ calculus and can therefore be used as input for strategy extraction algorithms. Experimental results illustrate the potential of the LDQ calculus in search-based QBF solving.

SAT Conference 2012 Conference Paper

Extended Failed-Literal Preprocessing for Quantified Boolean Formulas

Allen Van Gelder
Samuel B. Wood
Florian Lonsing

Abstract ~Building on recent work that adapts failed-literal analysis (FL) to Quantified Boolean Formulas (QBF), this paper introduces extended failed-literal analysis (EFL). FL and EFL are both preprocessing methods that apply a fast, but incomplete reasoning procedure to abstractions of the underlying QBF. EFL extends FL by remembering certain binary clauses that are implied by the same reasoning procedure as FL when it assumes one literal and that implies a second literal. This extension is almost free because the second literals are implied anyway during FL, but compared to analogous techniques for propositional satisfiability, its correctness involves some subtleties. For the first time, application of the universal pure literal rule is considered without also applying the existential pure literal rule. It is shown that using both pure literal rules in EFL is unsound. A modified reasoning procedure for QBF, called Unit-clause Propagation with Universal Pure literals (UPUP) is described and correctness is proved for EFL based on UPUP. Empirical results on the 568-benchmark suite of QBFEVAL-10 are presented.

SAT Conference 2012 Conference Paper

Resolution-Based Certificate Extraction for QBF - (Tool Presentation)

Aina Niemetz
Mathias Preiner
Florian Lonsing
Martina Seidl
Armin Biere

Abstract A certificate of (un)satisfiability for a quantified Boolean formula (QBF) represents sets of assignments to the variables, which act as witnesses for its truth value. Certificates are highly requested for practical applications of QBF like formal verification and model checking. We present an integrated set of tools realizing resolution-based certificate extraction for QBF in prenex conjunctive normal form. Starting from resolution proofs produced by the solver DepQBF, we describe the workflow consisting of proof checking, certificate extraction, and certificate checking. We implemented the steps of that workflow in stand-alone tools and carried out comprehensive experiments. Our results demonstrate the practical applicability of resolution-based certificate extraction.

SAT Conference 2011 Conference Paper

Failed Literal Detection for QBF

Florian Lonsing
Armin Biere

Abstract Failed literal detection (FL) in SAT is a powerful approach for preprocessing. The basic idea is to assign a variable as assumption. If boolean constraint propagation (BCP) yields an empty clause then the negated assumption is necessary for satisfiability. Whereas FL is common in SAT, it cannot easily be applied to QBF due to universal quantification. We present two approaches for FL to preprocess prenex CNFs. The first one is based on abstraction where certain universal variables are treated as existentially quantified. Second we combine QBF-specific BCP (QBCP) in FL with Q-resolution to validate assignments learnt by FL. Finally we compare these two approaches to a third common approach based on SAT. It turns out that the three approaches are incomparable. Experimental evaluation demonstrates that FL for QBF can improve the performance of search- and elimination-based QBF solvers.

SAT Conference 2010 Conference Paper

Automated Testing and Debugging of SAT and QBF Solvers

Robert Brummayer
Florian Lonsing
Armin Biere

Abstract Robustness and correctness are essential criteria for SAT and QBF solvers. We develop automated testing and debugging techniques designed and optimized for SAT and QBF solver development. Our fuzz testing techniques are able to find critical solver defects that lead to crashes, invalid satisfying assignments and incorrect satisfiability results. Moreover, we show that sequential and concurrent delta debugging techniques are highly effective in minimizing failure-inducing inputs.

SAT Conference 2010 Conference Paper

Integrating Dependency Schemes in Search-Based QBF Solvers

Florian Lonsing
Armin Biere

Abstract Many search-based QBF solvers implementing the DPLL algorithm for QBF (QDPLL) process formulae in prenex conjunctive normal form (PCNF). The quantifier prefix of PCNFs often results in strong variable dependencies which can influence solver performance negatively. A common approach to overcome this problem is to reconstruct quantifier structure e. g. by quantifier trees. Dependency schemes are a generalization of quantifier trees in the sense that more general dependency graphs can be obtained. So far, dependency graphs have not been applied in QBF solving. In this work we consider the problem of efficiently integrating dependency graphs in QDPLL. Thereby we generalize related work on integrating quantifier trees. By analyzing the core parts of QDPLL, we report on modifications necessary to profit from general dependency graphs. In comprehensive experiments we show that QDPLL using a particular dependency graph, despite of increased overhead, outperforms classical QDPLL relying on quantifier prefixes of PCNFs.

SAT Conference 2009 Conference Paper

A Compact Representation for Syntactic Dependencies in QBFs

Florian Lonsing
Armin Biere

Abstract Different quantifier types in Quantified Boolean Formulae (QBF) introduce variable dependencies which have to be taken into consideration when deciding satisfiability of a QBF. In this work, we focus on dependencies based on syntactically connected variables. We generalize our previous ideas for efficiently representing dependency sets of universal variables to existential ones. We obtain a dependency graph which is applicable to arbitrary QBF solvers. The core part of our work is the formulation and correctness proof of a static and compact, tree-shaped connection relation over equivalence classes of existential variables. In practice, this relation is constructed once from a given QBF and allows to share connection information among all variables. We report on practical aspects and demonstrate the effectiveness of our approach in experiments on structured formulae from QBF competitions. Further, we show by example that the common approach of quantifier scope analysis is not optimal among syntactic methods for dependency computation.

SAT Conference 2008 Conference Paper

Nenofex: Expanding NNF for QBF Solving

Florian Lonsing
Armin Biere

Abstract The topic of this paper is Nenofex, a solver for quantified boolean formulae (QBF) in negation normal form (NNF), which relies on expansion as the core technique for eliminating variables. In contrast to eliminating existentially quantified variables by resolution on CNF, which causes the formula size to increase quadratically in the worst case, expansion on NNF is involved with only a linear increase of the formula size. This property motivates the use of NNF instead of CNF combined with expansion. In Nenofex, a formula in NNF is represented as a tree with structural restrictions in order to keep its size small and distances from nodes to the root short. Expansions of variables are scheduled based on estimated expansion cost. The variable with the smallest estimated cost is expanded first. In order to remove redundancy from the formula, limited versions of two approaches from the domain of circuit optimization have been integrated. Experimental results on latest benchmarks show that Nenofex indeed exceeds a given memory limit less frequently than a resolution-based QBF solver for CNF, but also that there is the need for runtime-related improvements.