Related papers: Evaluating QBF Solvers: Quantifier Alternations Ma…
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…
Symmetries have been exploited successfully within the realms of SAT and QBF to improve solver performance in practical applications and to devise more powerful proof systems. As a first step towards extending these advancements to the…
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…
We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on experiments with a workflow to incrementally encode a planning instance into a sequence of…
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…
Current algorithms for bounded model checking use SAT methods for checking satisfiability of Boolean formulae. These methods suffer from the potential memory explosion problem. Methods based on the validity of Quantified Boolean Formulae…
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…
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…
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…
While symmetries are well understood for Boolean formulas and successfully exploited in practical SAT solving, less is known about symmetries in quantified Boolean formulas (QBF). There are some works introducing adaptions of propositional…
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 introduce a novel generalization of Counterexample-Guided Inductive Synthesis (CEGIS) and instantiate it to yield a novel, competitive algorithm for solving Quantified Boolean Formulas (QBF). Current QBF solvers based on…
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…
Dependency quantified Boolean formulas (DQBFs) are a powerful formalism, which subsumes quantified Boolean formulas (QBFs) and allows an explicit specification of dependencies of existential variables on universal variables. Driven by the…
Algebraic Normal Form (ANF) and Conjunctive Normal Form (CNF) are commonly used to encode problems in Boolean algebra. ANFs are typically solved via Gr"obner basis algorithms, often using more memory than is feasible; while CNFs are solved…
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…
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…
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…
This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…
This paper develops a parallel computational solver for computing all satifying assignments of a Boolean system of equations defined by Boolean functions of several variables. While there are we known solvers for satisfiability of Boolean…