3 Search Results for "Brandts, Alex"

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.146

Solving Promise Equations over Monoids and Groups

Authors: Alberto Larrauri and Stanislav Živný

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity classification for the same problem over groups.

Cite as

Alberto Larrauri and Stanislav Živný. Solving Promise Equations over Monoids and Groups. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 146:1-146:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{larrauri_et_al:LIPIcs.ICALP.2024.146,
  author =	{Larrauri, Alberto and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Solving Promise Equations over Monoids and Groups}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{146:1--146:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.146},
  URN =		{urn:nbn:de:0030-drops-202893},
  doi =		{10.4230/LIPIcs.ICALP.2024.146},
  annote =	{Keywords: constraint satisfaction, promise constraint satisfaction, equations, minions}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2021.121

Beyond PCSP(1-in-3, NAE)

Authors: Alex Brandts and Stanislav Živný

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract

The promise constraint satisfaction problem (PCSP) is a recently introduced vast generalisation of the constraint satisfaction problem (CSP) that captures approximability of satisfiable instances. A PCSP instance comes with two forms of each constraint: a strict one and a weak one. Given the promise that a solution exists using the strict constraints, the task is to find a solution using the weak constraints. While there are by now several dichotomy results for fragments of PCSPs, they all consider (in some way) symmetric PCSPs. 1-in-3-SAT and Not-All-Equal-3-SAT are classic examples of Boolean symmetric (non-promise) CSPs. While both problems are NP-hard, Brakensiek and Guruswami showed [SODA'18] that given a satisfiable instance of 1-in-3-SAT one can find a solution to the corresponding instance of (weaker) Not-All-Equal-3-SAT. In other words, the PCSP template (𝟏-in-𝟑,NAE) is tractable. We focus on non-symmetric PCSPs. In particular, we study PCSP templates obtained from the Boolean template (𝐭-in-𝐤, NAE) by either adding tuples to 𝐭-in-𝐤 or removing tuples from NAE. For the former, we classify all templates as either tractable or not solvable by the currently strongest known algorithm for PCSPs, the combined basic LP and affine IP relaxation of Brakensiek and Guruswami [SODA'20]. For the latter, we classify all templates as either tractable or NP-hard.

Cite as

Alex Brandts and Stanislav Živný. Beyond PCSP(1-in-3, NAE). In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 121:1-121:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{brandts_et_al:LIPIcs.ICALP.2021.121,
  author =	{Brandts, Alex and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Beyond PCSP(1-in-3, NAE)}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{121:1--121:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.121},
  URN =		{urn:nbn:de:0030-drops-141902},
  doi =		{10.4230/LIPIcs.ICALP.2021.121},
  annote =	{Keywords: promise constraint satisfaction, PCSP, polymorphisms, algebraic approach}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2020.17

The Complexity of Promise SAT on Non-Boolean Domains

Authors: Alex Brandts, Marcin Wrochna, and Stanislav Živný

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and Håstad [FOCS'14/SICOMP'17] proved a result known as "(2+ε)-SAT is NP-hard". They showed that the problem of distinguishing k-CNF formulas that are g-satisfiable (i.e. some assignment satisfies at least g literals in every clause) from those that are not even 1-satisfiable is NP-hard if g/k < 1/2 and is in P otherwise. We study a generalisation of SAT on arbitrary finite domains, with clauses that are disjunctions of unary constraints, and establish analogous behaviour. Thus we give a dichotomy for a natural fragment of promise constraint satisfaction problems (PCSPs) on arbitrary finite domains.

Cite as

Alex Brandts, Marcin Wrochna, and Stanislav Živný. The Complexity of Promise SAT on Non-Boolean Domains. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brandts_et_al:LIPIcs.ICALP.2020.17,
  author =	{Brandts, Alex and Wrochna, Marcin and \v{Z}ivn\'{y}, Stanislav},
  title =	{{The Complexity of Promise SAT on Non-Boolean Domains}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{17:1--17:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.17},
  URN =		{urn:nbn:de:0030-drops-124241},
  doi =		{10.4230/LIPIcs.ICALP.2020.17},
  annote =	{Keywords: promise constraint satisfaction, PCSP, polymorphisms, algebraic approach, label cover}
}

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3 Živný, Stanislav
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3 Theory of computation → Problems, reductions and completeness

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