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- Olaf Beyersdorff, Leroy Chew, Mikolás Janota
- STACS
- 2014

Proof systems for quantified Boolean formulas (QBFs) provide a theoretical underpinning for the performance of important QBF solvers. However, the proof complexity of these proof systems is currently not well understood and in particular lower bound techniques are missing. In this paper we exhibit a new and elegant proof technique for showing lower bounds… (More)

- Mikolás Janota, Leroy Chew, Olaf Beyersdorff
- Electronic Colloquium on Computational Complexity
- 2014

Several calculi for quantified Boolean formulas (QBFs) exist, but relations between them are not yet fully understood. This paper defines a novel calculus, which is resolutionbased and enables unification of the principal existing resolution-based QBF calculi, namely Q-resolution, long-distance Q-resolution and the expansion-based calculus ∀Exp+Res. All… (More)

- Olaf Beyersdorff, Leroy Chew, Karteek Sreenivasaiah
- LATA
- 2014

Article history: Received 25 June 2015 Received in revised form 6 October 2016 Accepted 27 November 2016 Available online xxxx

- Olaf Beyersdorff, Leroy Chew, Renate A. Schmidt, Martin Suda
- Electronic Colloquium on Computational Complexity
- 2016

We examine 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 the strict chain of proof systems Q-Res < IR-calc < IRM-calc, the situation is quite different in DQBF. The obvious… (More)

- Olaf Beyersdorff, Ilario Bonacina, Leroy Chew
- Electronic Colloquium on Computational Complexity
- 2015

A general and long-standing belief in the proof complexity community asserts that there is a close connection between progress in lower bounds for Boolean circuits and progress in proof size lower bounds for strong propositional proof systems. Although there are famous examples where a transfer from ideas and techniques from circuit complexity to proof… (More)

- Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla
- ICALP
- 2015

In sharp contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems. In this paper we establish the feasible interpolation technique for all resolution-based QBF systems, whether modelling CDCL or expansion-based solving. This both provides the first general lower bound method for QBF proof systems as well… (More)

- Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla
- STACS
- 2015

The groundbreaking paper ‘Short proofs are narrow – resolution made simple’ by Ben-Sasson and Wigderson (J. ACM 2001) introduces what is today arguably the main technique to obtain resolution lower bounds: to show a lower bound for the width of proofs. Another important measure for resolution is space, and in their fundamental work, Atserias and Dalmau (J.… (More)

- Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla
- FSTTCS
- 2016

We define a cutting planes system CP+∀red for quantified Boolean formulas (QBF) and analyse the proof-theoretic strength of this new calculus. While in the propositional case, Cutting Planes is of intermediate strength between resolution and Frege, our findings here show that the situation in QBF is slightly more complex: while CP+∀red is again weaker than… (More)

- Olaf Beyersdorff, Leroy Chew, Mikolás Janota
- Electronic Colloquium on Computational Complexity
- 2016

We investigate two QBF resolution systems that use extension variables: weak extended Q-resolution, where the extension variables are quantified at the innermost level, and extended Q-resolution, where the extension variables can be placed inside the quantifier prefix. These systems have been considered previously by (Jussila et al. 2007), who give… (More)

- Olaf Beyersdorff, Leroy Chew
- IJCAR
- 2014

We provide the first comprehensive proof-complexity analysis of different proof systems for propositional circumscription. In particular, we investigate two sequent-style calculi: MLK defined by Olivetti [28] and CIRC introduced by Bonatti and Olivetti [8], and the tableaux calculus NTAB suggested by Niemelä [26]. In our analysis we obtain exponential lower… (More)