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QRAT Polynomially Simulates Merge Resolution

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Sravanthi Chede, Anil Shukla

Computational Complexity · Submitted 20 Jul 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We further show that QRAT strictly p-simulates MRes.

how it is stated · asserted 1.00 read the record →

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arXiv ID2107.09320 (version 1)
Pith IDLQO67RGL, Pith's permanent record of this paper and its review
CitationAnil Shukla, Sravanthi Chede. "QRAT Polynomially Simulates Merge Resolution." arXiv:2107.09320 (2021). https://pith.science/paper/LQO67RGL
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 9,282 input tokens.

What the abstract itself states, as probabilities: claims first 0.88 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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 QRAT [Heule et al. J. Autom. Reason.'2017] proof system was designed to capture QBF preprocessing. QRAT can simulate both the expansion-based proof system $\forall$Exp+Res and CDCL-based QBF proof system LD-Q-Res. A family of false QBFs called SquaredEquality formulas were introduced in [Beyersdorff et al. J. Autom. Reason.'2021] and shown to be easy for MRes but need exponential size proofs in Q-Res, QU-Res, CP+$\forall$red, $\forall$Exp+Res, IR-calc and reductionless LD-Q-Res. As a result none of these systems can simulate MRes. In this paper, we show a short QRAT refutation of the SquaredEquality formulas. We further show that QRAT strictly p-simulates MRes. Besides highlighting the power of QRAT system, this work also presents the first simulation result for MRes.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Merge Resolution (MRes [Beyersdorff et al. J. Autom. background 1.00 0.03 0.01 unclear 0.87
s1 Reason.'2021] ) is a refutational proof system for quantified Boolean formulas (QBF). background 1.00 0.05 0.02 asserted 1.00
s2 Each line of MRes consists of clauses with only existential literals, together with information of countermodels stored as merge maps. background 1.00 0.07 0.02 asserted 1.00
s3 As a result, MRes has strategy extraction by design. background 0.86 0.08 0.02 asserted 1.00
s4 The QRAT [Heule et al. J. Autom. background 1.00 0.04 0.02 unclear 0.72
s5 Reason.'2017] proof system was designed to capture QBF preprocessing. background 1.00 0.04 0.02 asserted 1.00
s6 QRAT can simulate both the expansion-based proof system $\forall$Exp+Res and CDCL-based QBF proof system LD-Q-Res. background 0.99 0.10 0.04 asserted 1.00
s7 A family of false QBFs called SquaredEquality formulas were introduced in [Beyersdorff et al. J. Autom. background 0.99 0.09 0.02 asserted 1.00
s8 Reason.'2021] and shown to be easy for MRes but need exponential size proofs in Q-Res, QU-Res, CP+$\forall$red, $\forall$Exp+Res, IR-calc and reductionless LD-Q-Res. background 0.93 0.10 0.05 asserted 1.00
s9 As a result none of these systems can simulate MRes. interpretation 0.59 0.15 0.05 asserted 1.00
s10 In this paper, we show a short QRAT refutation of the SquaredEquality formulas. contribution 0.78 0.96 0.16 asserted 1.00
s11 We further show that QRAT strictly p-simulates MRes. result 0.85 0.96 0.90 asserted 1.00
s12 Besides highlighting the power of QRAT system, this work also presents the first simulation result for MRes. interpretation 0.62 0.81 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

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 QRAT [Heule et al. J. Autom. Reason.'2017] proof system was designed to capture QBF preprocessing. QRAT can simulate both the expansion-based proof system $\forall$Exp+Res and CDCL-based QBF proof system LD-Q-Res. A family of false QBFs called SquaredEquality formulas were introduced in [Beyersdorff et al. J. Autom. Reason.'2021] and shown to be easy for MRes but need exponential size proofs in Q-Res, QU-Res, CP+$\forall$red, $\forall$Exp+Res, IR-calc and reductionless LD-Q-Res. As a result none of these systems can simulate MRes. In this paper, we show a short QRAT refutation of the SquaredEquality formulas. We further show that QRAT strictly p-simulates MRes. Besides highlighting the power of QRAT system, this work also presents the first simulation result for MRes.

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