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.MFCS.2022.59
URN: urn:nbn:de:0030-drops-168575
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16857/
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Itsykson, Dmitry ; Riazanov, Artur

Automating OBDD proofs is NP-hard

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LIPIcs-MFCS-2022-59.pdf (0.8 MB)

Abstract

We prove that the proof system OBDD(∧, weakening) is not automatable unless P = NP. The proof is based upon the celebrated result of [Albert Atserias and Moritz Müller, 2019] about the hardness of automatability for resolution. The heart of the proof is lifting with multi-output indexing gadget from resolution block-width to dag-like multiparty number-in-hand communication protocol size with o(n) parties, where n is the number of variables in the non-lifted formula. A similar lifting theorem for protocols with n+1 participants was proved by [Göös et al., 2020] to establish the hardness of automatability result for Cutting Planes.

BibTeX - Entry

@InProceedings{itsykson_et_al:LIPIcs.MFCS.2022.59,
  author =	{Itsykson, Dmitry and Riazanov, Artur},
  title =	{{Automating OBDD proofs is NP-hard}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{59:1--59:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16857},
  URN =		{urn:nbn:de:0030-drops-168575},
  doi =		{10.4230/LIPIcs.MFCS.2022.59},
  annote =	{Keywords: proof complexity, OBDD, automatability, lifting, dag-like communication}
}

Keywords: proof complexity, OBDD, automatability, lifting, dag-like communication
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022

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