4 Search Results for "B�hm, Stanislav"

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.128
Linearly Ordered Colourings of Hypergraphs

Authors: Tamio-Vesa Nakajima and Stanislav Živný

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
A linearly ordered (LO) k-colouring of an r-uniform hypergraph assigns an integer from {1, …, k} to every vertex so that, in every edge, the (multi)set of colours has a unique maximum. Equivalently, for r = 3, if two vertices in an edge are assigned the same colour, then the third vertex is assigned a larger colour (as opposed to a different colour, as in classic non-monochromatic colouring). Barto, Battistelli, and Berg [STACS'21] studied LO colourings on 3-uniform hypergraphs in the context of promise constraint satisfaction problems (PCSPs). We show two results. First, given a 3-uniform hypergraph that admits an LO 2-colouring, one can find in polynomial time an LO k-colouring with k = O(√{nlog log n}/log n), where n is the number of vertices of the input hypergraph. This is established by building on ideas from algorithms designed for approximate graph colourings. Second, given an r-uniform hypergraph that admits an LO 2-colouring, we establish NP-hardness of finding an LO 3-colouring for every constant uniformity r ≥ 5. In fact, we determine the precise relationship of polymorphism minions for all uniformities r ≥ 3, which reveals a key difference between r = 3,4 and r ≥ 5 and which may be of independent interest. Using the algebraic approach to PCSPs, we actually show a more general result establishing NP-hardness of finding an LO (k+1)-colouring for LO k-colourable r-uniform hypergraphs for k ≥ 2 and r ≥ 5.
Cite as

Tamio-Vesa Nakajima and Stanislav Živný. Linearly Ordered Colourings of Hypergraphs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 128:1-128:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{nakajima_et_al:LIPIcs.ICALP.2022.128,
  author =	{Nakajima, Tamio-Vesa and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Linearly Ordered Colourings of Hypergraphs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{128:1--128:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.128},
  URN =		{urn:nbn:de:0030-drops-164692},
  doi =		{10.4230/LIPIcs.ICALP.2022.128},
  annote =	{Keywords: hypegraph colourings, promise constraint satisfaction, PCSP, polymorphisms, minions, algebraic approach}
}
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-dev.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
DOI: 10.4230/LIPIcs.MFCS.2019.60
Approximate Counting CSP Seen from the Other Side

Authors: Andrei A. Bulatov and Stanislav Živný

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
In this paper we study the complexity of counting Constraint Satisfaction Problems (CSPs) of the form #CSP(C,-), in which the goal is, given a relational structure A from a class C of structures and an arbitrary structure B, to find the number of homomorphisms from A to B. Flum and Grohe showed that #CSP(C,-) is solvable in polynomial time if C has bounded treewidth [FOCS'02]. Building on the work of Grohe [JACM'07] on decision CSPs, Dalmau and Jonsson then showed that, if C is a recursively enumerable class of relational structures of bounded arity, then assuming FPT != #W[1], there are no other cases of #CSP(C,-) solvable exactly in polynomial time (or even fixed-parameter time) [TCS'04]. We show that, assuming FPT != W[1] (under randomised parametrised reductions) and for C satisfying certain general conditions, #CSP(C,-) is not solvable even approximately for C of unbounded treewidth; that is, there is no fixed parameter tractable (and thus also not fully polynomial) randomised approximation scheme for #CSP(C,-). In particular, our condition generalises the case when C is closed under taking minors.
Cite as

Andrei A. Bulatov and Stanislav Živný. Approximate Counting CSP Seen from the Other Side. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bulatov_et_al:LIPIcs.MFCS.2019.60,
  author =	{Bulatov, Andrei A. and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Approximate Counting CSP Seen from the Other Side}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{60:1--60:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.60},
  URN =		{urn:nbn:de:0030-drops-110041},
  doi =		{10.4230/LIPIcs.MFCS.2019.60},
  annote =	{Keywords: constraint satisfaction, approximate counting, homomorphisms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.14
On Büchi One-Counter Automata

Authors: Stanislav Böhm, Stefan Göller, Simon Halfon, and Piotr Hofman

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract
Equivalence of deterministic pushdown automata is a famous problem in theoretical computer science whose decidability has been shown by Sénizergues. Our first result shows that decidability no longer holds when moving from finite words to infinite words. This solves an open problem that has recently been raised by Löding. In fact, we show that already the equivalence problem for deterministic Büchi one-counter automata is undecidable. Hence, the decidability border is rather tight when taking into account a recent result by Löding and Repke that equivalence of deterministic weak parity pushdown automata (a subclass of deterministic Büchi pushdown automata) is decidable. Another known result on finite words is that the universality problem for vector addition systems is decidable. We show undecidability when moving to infinite words. In fact, we prove that already the universality problem for nondeterministic Büchi one-counter nets (or equivalently vector addition systems with one unbounded dimension) is undecidable.
Cite as

Stanislav Böhm, Stefan Göller, Simon Halfon, and Piotr Hofman. On Büchi One-Counter Automata. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 14:1-14:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bohm_et_al:LIPIcs.STACS.2017.14,
  author =	{B\"{o}hm, Stanislav and G\"{o}ller, Stefan and Halfon, Simon and Hofman, Piotr},
  title =	{{On B\"{u}chi One-Counter Automata}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{14:1--14:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.14},
  URN =		{urn:nbn:de:0030-drops-70194},
  doi =		{10.4230/LIPIcs.STACS.2017.14},
  annote =	{Keywords: infinite words, deterministic pushdown automata}
}
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