License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SAT.2023.27
URN: urn:nbn:de:0030-drops-184894
URL: https://drops.dagstuhl.de/opus/volltexte/2023/18489/
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Vinyals, Marc ; Li, Chunxiao ; Fleming, Noah ; Kolokolova, Antonina ; Ganesh, Vijay

Limits of CDCL Learning via Merge Resolution

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LIPIcs-SAT-2023-27.pdf (0.7 MB)


Abstract

In their seminal work, Atserias et al. and independently Pipatsrisawat and Darwiche in 2009 showed that CDCL solvers can simulate resolution proofs with polynomial overhead. However, previous work does not address the tightness of the simulation, i.e., the question of how large this overhead needs to be. In this paper, we address this question by focusing on an important property of proofs generated by CDCL solvers that employ standard learning schemes, namely that the derivation of a learned clause has at least one inference where a literal appears in both premises (aka, a merge literal). Specifically, we show that proofs of this kind can simulate resolution proofs with at most a linear overhead, but there also exist formulas where such overhead is necessary or, more precisely, that there exist formulas with resolution proofs of linear length that require quadratic CDCL proofs.

BibTeX - Entry

@InProceedings{vinyals_et_al:LIPIcs.SAT.2023.27,
  author =	{Vinyals, Marc and Li, Chunxiao and Fleming, Noah and Kolokolova, Antonina and Ganesh, Vijay},
  title =	{{Limits of CDCL Learning via Merge Resolution}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{27:1--27:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18489},
  URN =		{urn:nbn:de:0030-drops-184894},
  doi =		{10.4230/LIPIcs.SAT.2023.27},
  annote =	{Keywords: proof complexity, resolution, merge resolution, CDCL, learning scheme}
}

Keywords: proof complexity, resolution, merge resolution, CDCL, learning scheme
Collection: 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)
Issue Date: 2023
Date of publication: 09.08.2023


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