4 Search Results for "Ovcharov, Sergei"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.81
Supercritical Tradeoff Between Size and Depth for Resolution over Parities

Authors: Dmitry Itsykson and Alexander Knop

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Alekseev and Itsykson (STOC 2025) proved the existence of an unsatisfiable CNF formula such that any resolution over parities (Res(⊕)) refutation must either have exponential size (in the formula size) or superlinear depth (in the number of variables). In this paper, we extend this result by constructing a formula with the same hardness properties, but which additionally admits a resolution refutation of quasi-polynomial size. This establishes a supercritical tradeoff between size and depth for resolution over parities. The proof builds on the framework of Alekseev and Itsykson and relies on a lifting argument applied to the supercritical tradeoff between width and depth in resolution, proposed by Buss and Thapen (IPL 2026).
Cite as

Dmitry Itsykson and Alexander Knop. Supercritical Tradeoff Between Size and Depth for Resolution over Parities. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 81:1-81:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{itsykson_et_al:LIPIcs.ITCS.2026.81,
  author =	{Itsykson, Dmitry and Knop, Alexander},
  title =	{{Supercritical Tradeoff Between Size and Depth for Resolution over Parities}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{81:1--81:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.81},
  URN =		{urn:nbn:de:0030-drops-253680},
  doi =		{10.4230/LIPIcs.ITCS.2026.81},
  annote =	{Keywords: lifting theorems, resolution depth, resolution over parities, resolution width, supercritical tradeoff}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.8
Amortized Closure and Its Applications in Lifting for Resolution over Parities

Authors: Klim Efremenko and Dmitry Itsykson

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
The notion of closure of a set of linear forms, first introduced by Efremenko, Garlik, and Itsykson [Klim Efremenko et al., 2024], has proven instrumental in proving lower bounds on the sizes of regular and bounded-depth Res(⊕) refutations [Klim Efremenko et al., 2024; Yaroslav Alekseev and Dmitry Itsykson, 2025]. In this work, we present amortized closure, an enhancement that retains the properties of original closure [Klim Efremenko et al., 2024] but offers tighter control on its growth. Specifically, adding a new linear form increases the amortized closure by at most one. We explore two applications that highlight the power of this new concept. Utilizing our newly defined amortized closure, we extend and provide a succinct and elegant proof of the recent lifting theorem by Chattopadhyay and Dvorak [Arkadev Chattopadhyay and Pavel Dvorak, 2025]. Namely we show that for an unsatisfiable CNF formula φ and a 1-stifling gadget g: {0,1}^𝓁 → {0,1}, if the lifted formula φ∘g has a tree-like Res(⊕) refutation of size 2^d and width w, then φ has a resolution refutation of depth d and width w. The original theorem by Chattopadhyay and Dvorak [Arkadev Chattopadhyay and Pavel Dvorak, 2025] applies only to the more restrictive class of strongly stifling gadgets. As a more significant application of amortized closure, we show improved lower bounds for bounded-depth Res(⊕), extending the depth beyond that of Alekseev and Itsykson [Yaroslav Alekseev and Dmitry Itsykson, 2025]. Our result establishes an exponential lower bound for depth-Ω(n log n) Res(⊕) refutations of lifted Tseitin formulas, a notable improvement over the existing depth-Ω(n log log n) Res(⊕) lower bound.
Cite as

Klim Efremenko and Dmitry Itsykson. Amortized Closure and Its Applications in Lifting for Resolution over Parities. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 8:1-8:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{efremenko_et_al:LIPIcs.CCC.2025.8,
  author =	{Efremenko, Klim and Itsykson, Dmitry},
  title =	{{Amortized Closure and Its Applications in Lifting for Resolution over Parities}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{8:1--8:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.8},
  URN =		{urn:nbn:de:0030-drops-237023},
  doi =		{10.4230/LIPIcs.CCC.2025.8},
  annote =	{Keywords: lifting, resolution over parities, closure of linear forms, lower bounds, width, depth, size vs depth tradeoff}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.19
On Limits of Symbolic Approach to SAT Solving

Authors: Dmitry Itsykson and Sergei Ovcharov

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
We study the symbolic approach to the propositional satisfiability problem proposed by Aguirre and Vardi in 2001 based on OBDDs and symbolic quantifier elimination. We study the theoretical limitations of the most general version of this approach where it is allowed to dynamically change variable order in OBDD. We refer to algorithms based on this approach as OBDD(∧, ∃, reordering) algorithms. We prove the first exponential lower bound of OBDD(∧, ∃, reordering) algorithms on unsatisfiable formulas, and give an example of formulas having short tree-like resolution proofs that are exponentially hard for OBDD(∧, ∃, reordering) algorithms. We also present the first exponential lower bound for natural formulas with clear combinatorial meaning: every OBDD(∧, ∃, reordering) algorithm runs exponentially long on the binary pigeonhole principle BPHP^{n+1}_n.
Cite as

Dmitry Itsykson and Sergei Ovcharov. On Limits of Symbolic Approach to SAT Solving. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 19:1-19:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{itsykson_et_al:LIPIcs.SAT.2024.19,
  author =	{Itsykson, Dmitry and Ovcharov, Sergei},
  title =	{{On Limits of Symbolic Approach to SAT Solving}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{19:1--19:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.19},
  URN =		{urn:nbn:de:0030-drops-205415},
  doi =		{10.4230/LIPIcs.SAT.2024.19},
  annote =	{Keywords: Symbolic quantifier elimination, OBDD, lower bounds, tree-like resolution, proof complexity, error-correcting codes, binary pigeonhole principle}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.72
OBDD(Join) Proofs Cannot Be Balanced

Authors: Sergei Ovcharov

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
We study OBDD-based propositional proof systems introduced in 2004 by Atserias, Kolaitis, and Vardi that prove the unsatisfiability of a CNF formula by deduction of an identically false OBDD from OBDDs representing clauses of the initial formula. We consider a proof system OBDD(∧) that uses only the conjunction (join) rule and a proof system OBDD(∧, reordering) (introduced in 2017 by Itsykson, Knop, Romashchenko, and Sokolov) that uses the conjunction (join) rule and the rule that allows changing the order of variables in OBDD. We study whether these systems can be balanced i.e. every refutation of size S can be reassembled into a refutation of depth O(log S) with at most a polynomial-size increase. We construct a family of unsatisfiable CNF formulas F_n such that F_n has a polynomial-size tree-like OBDD(∧) refutation of depth poly(n) and for arbitrary OBDD(∧, reordering) refutation Π of F_n for every α ∈ (0,1) the following trade-off holds: either the size of Π is 2^Ω(n^α) or the depth of Π is Ω(n^{1-α}). As a corollary of the trade-offs, we get that OBDD(∧) and OBDD(∧, reordering) proofs cannot be balanced.
Cite as

Sergei Ovcharov. OBDD(Join) Proofs Cannot Be Balanced. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 72:1-72:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{ovcharov:LIPIcs.MFCS.2023.72,
  author =	{Ovcharov, Sergei},
  title =	{{OBDD(Join) Proofs Cannot Be Balanced}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{72:1--72:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.72},
  URN =		{urn:nbn:de:0030-drops-186065},
  doi =		{10.4230/LIPIcs.MFCS.2023.72},
  annote =	{Keywords: Proof complexity, OBDD, lower bounds, depth of proofs}
}
  • Refine by Type
  • 4 Document/PDF
  • 2 Document/HTML

  • Refine by Publication Year
  • 1 2026
  • 1 2025
  • 1 2024
  • 1 2023

  • Refine by Author
  • 3 Itsykson, Dmitry
  • 2 Ovcharov, Sergei
  • 1 Efremenko, Klim
  • 1 Knop, Alexander

  • Refine by Series/Journal
  • 4 LIPIcs

  • Refine by Classification
  • 4 Theory of computation → Proof complexity

  • Refine by Keyword
  • 3 lower bounds
  • 2 OBDD
  • 2 resolution over parities
  • 1 Proof complexity
  • 1 Symbolic quantifier elimination
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact