Related papers: An Achilles' Heel of Term-Resolution
Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as…
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…
A quantified Boolean formula (QBF) is a propositional formula extended with universal and existential quantification over propositions. There are two methodologies in CEGAR based QBF solving techniques, one that is based on a refinement…
QBF solvers implementing the QCDCL paradigm are powerful algorithms that successfully tackle many computationally complex applications. However, our theoretical understanding of the strength and limitations of these QCDCL solvers is very…
We examine the existing Resolution systems for quantified Boolean formulas (QBF) and answer the question which of these calculi can be lifted to the more powerful Dependency QBFs (DQBF). An interesting picture emerges: While for QBF we have…
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…
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…
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…
Determining the validity of a quantified Boolean formula (QBF) is a PSPACE-complete problem with rich expressive power. Despite interest in efficient solvers, there is, compared to problems in NP, a lack of positive theoretical results, and…
We exploit symmetries to give short proofs for two prominent formula families of QBF proof complexity. On the one hand, we employ symmetry breakers. On the other hand, we enrich the (relatively weak) QBF resolution calculus Q-Res with the…
We prove the first genuine QBF proof size lower bounds for the proof system Merge Resolution (MRes [Olaf Beyersdorff et al., 2020]), a refutational proof system for prenex quantified Boolean formulas (QBF) with a CNF matrix. Unlike most QBF…
Merge Resolution (MRes [Beyersdorff et al. J. Autom. Reason.'2021] ) is a refutational proof system for quantified Boolean formulas (QBF). Each line of MRes consists of clauses with only existential literals, together with information of…
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…
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…
We introduce and investigate symbolic proof systems for Quantified Boolean Formulas (QBF) operating on Ordered Binary Decision Diagrams (OBDDs). These systems capture QBF solvers that perform symbolic quantifier elimination, and as such…
We propose reductions to quantified Boolean formulas (QBF) as a new approach to showing fixed-parameter linear algorithms for problems parameterized by treewidth. We demonstrate the feasibility of this approach by giving new algorithms for…
The aim of this PhD project is to develop fast and robust reasoning tools for dependency quantified Boolean formulas (DQBF). In this paper, we outline two properties, autarkies and symmetries, that potentially can be exploited for pre- and…
Quantified Boolean formulas (QBFs) generalize propositional formulas by admitting quantifications over propositional variables. QBFs can be viewed as (restricted) formulas of first-order predicate logic and easy translations of QBFs into…
We introduce new semi-algebraic proof systems for Quantified Boolean Formulas (QBF) analogous to the propositional systems Nullstellensatz, Sherali-Adams and Sum-of-Squares. We transfer to this setting techniques both from the QBF…
We pioneer a new technique that allows us to prove a multitude of previously open simulations in QBF proof complexity. In particular, we show that extended QBF Frege p-simulates clausal proof systems such as IR-Calculus, IRM-Calculus,…