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Electronic Colloquium on Computational Complexity

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All reports by Author Anil Shukla:

TR17-037 | 25th February 2017
Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla

Understanding Cutting Planes for QBFs

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 >>>

TR16-164 | 25th October 2016
Andreas Krebs, Meena Mahajan, Anil Shukla

Relating two width measures for resolution proofs

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 >>>

TR15-152 | 16th September 2015
Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla

Are Short Proofs Narrow? QBF Resolution is not Simple.

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 >>>

TR15-059 | 10th April 2015
Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla

Feasible Interpolation for QBF Resolution Calculi

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 >>>

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