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During the last two decades, an active line of research in proof complexity has been into the space complexity of proofs and how space is related to other measures.By now these aspects of the resolution proof system are fairly well understood, but many open problems remain for the related but stronger proof system polynomial calculus (PC/PCR).For instance, the space complexity of many standard "benchmark formulas" is still open, as well as the relation of space to size and degree in PC/PCR.We prove that if a formula requires large resolution width, then making XOR substitution yields a formula requiring large PCR space (and hence also PC space), providing some circumstantial evidence that degree might be a lower bound for

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Publication Details

Journal
Theory of Computing
Published
2025-01-01
DOI
https://doi.org/10.4086/toc.2025.v021a004
Primary Topic
Complexity and Algorithms in Graphs
Type
article
Field-Weighted Citation Impact
0.00

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Jakob Nordstr”öm, Marc Vinyals, Massimo Lauria, Yuval Filmus et al.
Theory of Computing
Complexity and Algorithms in Graphs
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Jakob Nordstr”öm, Marc Vinyals, Massimo Lauria, Yuval Filmus, Mladen Mikša
article en

Abstract

During the last two decades, an active line of research in proof complexity has been into the space complexity of proofs and how space is related to other measures.By now these aspects of the resolution proof system are fairly well understood, but many open problems remain for the related but stronger proof system polynomial calculus (PC/PCR).For instance, the space complexity of many standard "benchmark formulas" is still open, as well as the relation of space to size and degree in PC/PCR.We prove that if a formula requires large resolution width, then making XOR substitution yields a formula requiring large PCR space (and hence also PC space), providing some circumstantial evidence that degree might be a lower bound for

Theory of ComputingVol. 21(1)
European Commission, University of Toronto, Kungliga Tekniska Högskolan, Vetenskapsrådet
Openalex Percentile: Top 76%
Complexity and Algorithms in Graphs
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