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REPORTS > AUTHORS > OLAF BEYERSDORFF:
All reports by Author Olaf Beyersdorff:

TR24-038 | 27th February 2024
Olaf Beyersdorff, Kaspar Kasche, Luc Nicolas Spachmann

Polynomial Calculus for Quantified Boolean Logic: Lower Bounds through Circuits and Degree

We initiate an in-depth proof-complexity analysis of polynomial calculus (Q-PC) for Quantified Boolean Formulas (QBF). In the course of this we establish a tight proof-size characterisation of Q-PC in terms of a suitable circuit model (polynomial decision lists). Using this correspondence we show a size-degree relation for Q-PC, similar in ... more >>>


TR24-030 | 22nd February 2024
Olaf Beyersdorff, Tim Hoffmann, Luc Nicolas Spachmann

Proof Complexity of Propositional Model Counting

Recently, the proof system MICE for the model counting problem #SAT was introduced by Fichte, Hecher and Roland (SAT’22). As demonstrated by Fichte et al., the system MICE can be used for proof logging for state-of-the-art #SAT solvers.
We perform a proof-complexity study of MICE. For this we first simplify ... more >>>


TR23-051 | 18th April 2023
Benjamin Böhm, Olaf Beyersdorff

QCDCL vs QBF Resolution: Further Insights

We continue the investigation on the relations of QCDCL and QBF resolution systems. In particular, we introduce QCDCL versions that tightly characterise QU-Resolution and (a slight variant of) long-distance Q-Resolution. We show that most QCDCL variants - parameterised by different policies for decisions, unit propagations and reductions -- lead to ... more >>>


TR22-040 | 10th March 2022
Benjamin Böhm, Tomáš Peitl, Olaf Beyersdorff

Should decisions in QCDCL follow prefix order?

Quantified conflict-driven clause learning (QCDCL) is one of the main solving approaches for quantified Boolean formulas (QBF). One of the differences between QCDCL and propositional CDCL is that QCDCL typically follows the prefix order of the QBF for making decisions.
We investigate an alternative model for QCDCL solving where decisions ... more >>>


TR22-036 | 10th March 2022
Agnes Schleitzer, Olaf Beyersdorff

Classes of Hard Formulas for QBF Resolution

Revisions: 1

To date, we know only a few handcrafted quantified Boolean formulas (QBFs) that are hard for central QBF resolution systems such as Q and QU, and only one specific QBF family to separate Q and QU.

Here we provide a general method to construct hard formulas for Q and ... more >>>


TR21-135 | 6th September 2021
Olaf Beyersdorff, Joshua Blinkhorn, Tomáš Peitl

Strong (D)QBF Dependency Schemes via Implication-free Resolution Paths

We suggest a general framework to study dependency schemes for dependency quantified Boolean formulas (DQBF). As our main contribution, we exhibit a new infinite collection of implication-free DQBF dependency schemes that generalise the reflexive resolution path dependency scheme. We establish soundness of all these schemes, implying that they can be ... more >>>


TR21-131 | 10th September 2021
Olaf Beyersdorff, Benjamin Böhm

QCDCL with Cube Learning or Pure Literal Elimination - What is best?

Revisions: 1

Quantified conflict-driven clause learning (QCDCL) is one of the main approaches for solving quantified Boolean formulas (QBF). We formalise and investigate several versions of QCDCL that include cube learning and/or pure-literal elimination, and formally compare the resulting solving models via proof complexity techniques. Our results show that almost all of ... more >>>


TR20-188 | 12th December 2020
Olaf Beyersdorff, Joshua Blinkhorn, Meena Mahajan, Tomáš Peitl, Gaurav Sood

Hard QBFs for Merge Resolution

Revisions: 1

We prove the first 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 resolution systems in the literature, proofs in MRes consist of resolution steps together ... more >>>


TR20-053 | 16th April 2020
Olaf Beyersdorff, Benjamin Böhm

Understanding the Relative Strength of QBF CDCL Solvers and QBF Resolution

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 limited.

In this paper we suggest to formally model QCDCL solvers as proof systems. We
define different policies that ... more >>>


TR20-036 | 9th March 2020
Olaf Beyersdorff, Joshua Blinkhorn, Tomáš Peitl

Strong (D)QBF Dependency Schemes via Tautology-free Resolution Paths

We suggest a general framework to study dependency schemes for dependency quantified Boolean formulas (DQBF). As our main contribution, we exhibit a new tautology-free DQBF dependency scheme that generalises the reflexive resolution path dependency scheme. We establish soundness of the tautology-free scheme, implying that it can be used in any ... more >>>


TR20-005 | 17th January 2020
Olaf Beyersdorff, Joshua Blinkhorn, Meena Mahajan

Hardness Characterisations and Size-Width Lower Bounds for QBF Resolution

Revisions: 1

We provide a tight characterisation of proof size in resolution for quantified Boolean formulas (QBF) by circuit complexity. Such a characterisation was previously obtained for a hierarchy of QBF Frege systems (Beyersdorff & Pich, LICS 2016), but leaving open the most important case of QBF resolution. Different from the Frege ... more >>>


TR19-057 | 6th April 2019
Olaf Beyersdorff, Joshua Blinkhorn

Proof Complexity of Symmetry Learning in QBF

For quantified Boolean formulas (QBF), a resolution system with a symmetry rule was recently introduced by Kauers and Seidl (Inf. Process. Lett. 2018). In this system, many formulas hard for QBF resolution admit short proofs.

Kauers and Seidl apply the symmetry rule on symmetries of the original formula. Here we ... more >>>




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