All reports by Author Anil Shukla:

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TR23-129
| 21st August 2023
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Sravanthi Chede, Leroy Chew, Balesh Kumar, Anil Shukla#### Understanding Nullstellensatz for QBFs

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TR22-002
| 11th December 2021
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Sravanthi Chede, Anil Shukla#### Extending Merge Resolution to a Family of Proof Systems

Revisions: 1

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TR21-109
| 20th July 2021
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Sravanthi Chede, Anil Shukla#### QRAT Polynomially Simulates Merge Resolution.

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TR21-104
| 26th June 2021
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Sravanthi Chede, Anil Shukla#### Does QRAT simulate IR-calc? QRAT simulation algorithm for $\forall$Exp+Res cannot be lifted to IR-calc

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TR17-037
| 25th February 2017
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Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla#### Understanding Cutting Planes for QBFs

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TR16-164
| 25th October 2016
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Andreas Krebs, Meena Mahajan, Anil Shukla#### Relating two width measures for resolution proofs

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TR15-152
| 16th September 2015
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Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla#### Are Short Proofs Narrow? QBF Resolution is not Simple.

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TR15-059
| 10th April 2015
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Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla#### Feasible Interpolation for QBF Resolution Calculi

Sravanthi Chede, Leroy Chew, Balesh Kumar, Anil Shukla

QBF proof systems are routinely adapted from propositional logic along with adjustments for the new quantifications. Existing are two main successful frameworks, the reduction and expansion frameworks, inspired by QCDCL [Zhang et al. ICCAD.'2002] and CEGAR solving [Janota et al. Artif. Intell.'2016] respectively. However, the reduction framework, while immensely useful ... more >>>

Sravanthi Chede, Anil Shukla

Merge Resolution (MRes [Beyersdorff et al. J. Autom. Reason.'2021]) is a recently introduced proof system for false QBFs. Unlike other known QBF proof systems, it builds winning strategies for the universal player within the proofs. Every line of this proof system consists of existential clauses along with countermodels. MRes stores ... more >>>

Sravanthi Chede, Anil Shukla

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 countermodels stored as merge maps. As a result, MRes has strategy extraction by design. The ... more >>>

Sravanthi Chede, Anil Shukla

We show that the QRAT simulation algorithm of $\forall$Exp+Res from [B. Kiesl and M. Seidl, 2019] cannot be lifted to IR-calc.

more >>>Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla

We define a cutting planes system CP+$\forall$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 ... more >>>

Andreas Krebs, Meena Mahajan, Anil Shukla

In this short note, we revisit two hardness measures for resolution proofs: width and asymmetric width. It is known that for every unsatisfiable CNF F,

width(F \derives \Box) \le awidth(F \derives \Box) + max{ awidth(F \derives \Box), width(F)}.

We give a simple direct proof of the upper bound, ... more >>>

Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla

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 ... more >>>

Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla

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 ... more >>>