5 Search Results for "Wiebking, Daniel"


Document
Lower Bounds for Choiceless Polynomial Time via Symmetric XOR-Circuits

Authors: Benedikt Pago

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


Abstract
Choiceless Polynomial Time (CPT) is one of the few remaining candidate logics for capturing Ptime. In this paper, we make progress towards separating CPT from polynomial time by firstly establishing a connection between the expressive power of CPT and the existence of certain symmetric circuit families, and secondly, proving lower bounds against these circuits. We focus on the isomorphism problem of unordered Cai-Fürer-Immerman-graphs (the CFI-query) as a potential candidate for separating CPT from Ptime. Results by Dawar, Richerby and Rossman, and subsequently by Pakusa, Schalthöfer and Selman show that the CFI-query is CPT-definable on linearly ordered and preordered base graphs with small colour classes. We define a class of CPT-algorithms, that we call "CFI-symmetric algorithms", which generalises all the known ones, and show that such algorithms can only define the CFI-query on a given class of base graphs if there exists a family of symmetric XOR-circuits with certain properties. These properties include that the circuits have the same symmetries as the base graphs, are of polynomial size, and satisfy certain fan-in restrictions. Then we prove that such circuits with slightly strengthened requirements (i.e. stronger symmetry and fan-in and fan-out restrictions) do not exist for the n-dimensional hypercubes as base graphs. This almost separates the CFI-symmetric algorithms from Ptime - up to the gap that remains between the circuits whose existence we can currently disprove and the circuits whose existence is necessary for the definability of the CFI-query by a CFI-symmetric algorithm.

Cite as

Benedikt Pago. Lower Bounds for Choiceless Polynomial Time via Symmetric XOR-Circuits. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 73:1-73:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{pago:LIPIcs.MFCS.2023.73,
  author =	{Pago, Benedikt},
  title =	{{Lower Bounds for Choiceless Polynomial Time via Symmetric XOR-Circuits}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{73:1--73:15},
  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.2023.73},
  URN =		{urn:nbn:de:0030-drops-186077},
  doi =		{10.4230/LIPIcs.MFCS.2023.73},
  annote =	{Keywords: logic in computer science, finite model theory, descriptive complexity, symmetric computation, symmetric circuits, graph isomorphism}
}
Document
Finite Model Theory and Proof Complexity Revisited: Distinguishing Graphs in Choiceless Polynomial Time and the Extended Polynomial Calculus

Authors: Benedikt Pago

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)


Abstract
This paper extends prior work on the connections between logics from finite model theory and propositional/algebraic proof systems. We show that if all non-isomorphic graphs in a given graph class can be distinguished in the logic Choiceless Polynomial Time with counting (CPT), then they can also be distinguished in the bounded-degree extended polynomial calculus (EPC), and the refutations have roughly the same size as the resource consumption of the CPT-sentence. This allows to transfer lower bounds for EPC to CPT and thus constitutes a new potential approach towards better understanding the limits of CPT. A super-polynomial EPC lower bound for a Ptime-instance of the graph isomorphism problem would separate CPT from Ptime and thus solve a major open question in finite model theory. Further, using our result, we provide a model theoretic proof for the separation of bounded-degree polynomial calculus and bounded-degree extended polynomial calculus.

Cite as

Benedikt Pago. Finite Model Theory and Proof Complexity Revisited: Distinguishing Graphs in Choiceless Polynomial Time and the Extended Polynomial Calculus. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{pago:LIPIcs.CSL.2023.31,
  author =	{Pago, Benedikt},
  title =	{{Finite Model Theory and Proof Complexity Revisited: Distinguishing Graphs in Choiceless Polynomial Time and the Extended Polynomial Calculus}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.31},
  URN =		{urn:nbn:de:0030-drops-174923},
  doi =		{10.4230/LIPIcs.CSL.2023.31},
  annote =	{Keywords: finite model theory, proof complexity, graph isomorphism}
}
Document
Track A: Algorithms, Complexity and Games
Hypergraph Isomorphism for Groups with Restricted Composition Factors

Authors: Daniel Neuen

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


Abstract
We consider the isomorphism problem for hypergraphs taking as input two hypergraphs over the same set of vertices V and a permutation group Γ over domain V, and asking whether there is a permutation γ ∈ Γ that proves the two hypergraphs to be isomorphic. We show that for input groups, all of whose composition factors are isomorphic to a subgroup of the symmetric group on d points, this problem can be solved in time (n+m)^O((log d)^c) for some absolute constant c where n denotes the number of vertices and m the number of hyperedges. In particular, this gives the currently fastest isomorphism test for hypergraphs in general. The previous best algorithm for the above problem due to Schweitzer and Wiebking (STOC 2019) runs in time n^O(d)m^O(1). As an application of this result, we obtain, for example, an algorithm testing isomorphism of graphs excluding K_{3,h} as a minor in time n^O((log h)^c). In particular, this gives an isomorphism test for graphs of Euler genus at most g running in time n^O((log g)^c).

Cite as

Daniel Neuen. Hypergraph Isomorphism for Groups with Restricted Composition Factors. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 88:1-88:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{neuen:LIPIcs.ICALP.2020.88,
  author =	{Neuen, Daniel},
  title =	{{Hypergraph Isomorphism for Groups with Restricted Composition Factors}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{88:1--88:19},
  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.2020.88},
  URN =		{urn:nbn:de:0030-drops-124959},
  doi =		{10.4230/LIPIcs.ICALP.2020.88},
  annote =	{Keywords: graph isomorphism, groups with restricted composition factors, hypergraphs, bounded genus graphs}
}
Document
Track A: Algorithms, Complexity and Games
Graph Isomorphism in Quasipolynomial Time Parameterized by Treewidth

Authors: Daniel Wiebking

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


Abstract
We extend Babai’s quasipolynomial-time graph isomorphism test (STOC 2016) and develop a quasipolynomial-time algorithm for the multiple-coset isomorphism problem. The algorithm for the multiple-coset isomorphism problem allows to exploit graph decompositions of the given input graphs within Babai’s group-theoretic framework. We use it to develop a graph isomorphism test that runs in time n^polylog(k) where n is the number of vertices and k is the minimum treewidth of the given graphs and polylog(k) is some polynomial in log(k). Our result generalizes Babai’s quasipolynomial-time graph isomorphism test.

Cite as

Daniel Wiebking. Graph Isomorphism in Quasipolynomial Time Parameterized by Treewidth. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 103:1-103:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{wiebking:LIPIcs.ICALP.2020.103,
  author =	{Wiebking, Daniel},
  title =	{{Graph Isomorphism in Quasipolynomial Time Parameterized by Treewidth}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{103:1--103:16},
  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.2020.103},
  URN =		{urn:nbn:de:0030-drops-125106},
  doi =		{10.4230/LIPIcs.ICALP.2020.103},
  annote =	{Keywords: Graph isomorphism, canonization, treewidth, hypergraphs}
}
Document
An Improved Isomorphism Test for Bounded-Tree-Width Graphs

Authors: Martin Grohe, Daniel Neuen, Pascal Schweitzer, and Daniel Wiebking

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
We give a new fpt algorithm testing isomorphism of n-vertex graphs of tree width k in time 2^{k polylog(k)} poly n, improving the fpt algorithm due to Lokshtanov, Pilipczuk, Pilipczuk, and Saurabh (FOCS 2014), which runs in time 2^{O(k^5 log k)}poly n. Based on an improved version of the isomorphism-invariant graph decomposition technique introduced by Lokshtanov et al., we prove restrictions on the structure of the automorphism groups of graphs of tree width k. Our algorithm then makes heavy use of the group theoretic techniques introduced by Luks (JCSS 1982) in his isomorphism test for bounded degree graphs and Babai (STOC 2016) in his quasipolynomial isomorphism test. In fact, we even use Babai's algorithm as a black box in one place. We give a second algorithm which, at the price of a slightly worse run time 2^{O(k^2 log k)}poly n, avoids the use of Babai's algorithm and, more importantly, has the additional benefit that it can also be used as a canonization algorithm.

Cite as

Martin Grohe, Daniel Neuen, Pascal Schweitzer, and Daniel Wiebking. An Improved Isomorphism Test for Bounded-Tree-Width Graphs. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{grohe_et_al:LIPIcs.ICALP.2018.67,
  author =	{Grohe, Martin and Neuen, Daniel and Schweitzer, Pascal and Wiebking, Daniel},
  title =	{{An Improved Isomorphism Test for Bounded-Tree-Width Graphs}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{67:1--67:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.67},
  URN =		{urn:nbn:de:0030-drops-90714},
  doi =		{10.4230/LIPIcs.ICALP.2018.67},
  annote =	{Keywords: graph isomorphism, graph canonization, tree width, decompositions}
}
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