9 Search Results for "Kiefer, Sandra"

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.156
Verification of Population Protocols with Unordered Data

Authors: Steffen van Bergerem, Roland Guttenberg, Sandra Kiefer, Corto Mascle, Nicolas Waldburger, and Chana Weil-Kennedy

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

Abstract
Population protocols are a well-studied model of distributed computation in which a group of anonymous finite-state agents communicates via pairwise interactions. Together they decide whether their initial configuration, i. e., the initial distribution of agents in the states, satisfies a property. As an extension in order to express properties of multisets over an infinite data domain, Blondin and Ladouceur (ICALP'23) introduced population protocols with unordered data (PPUD). In PPUD, each agent carries a fixed data value, and the interactions between agents depend on whether their data are equal or not. Blondin and Ladouceur also identified the interesting subclass of immediate observation PPUD (IOPPUD), where in every transition one of the two agents remains passive and does not move, and they characterised its expressive power. We study the decidability and complexity of formally verifying these protocols. The main verification problem for population protocols is well-specification, that is, checking whether the given PPUD computes some function. We show that well-specification is undecidable in general. By contrast, for IOPPUD, we exhibit a large yet natural class of problems, which includes well-specification among other classic problems, and establish that these problems are in ExpSpace. We also provide a lower complexity bound, namely coNExpTime-hardness.
Cite as

Steffen van Bergerem, Roland Guttenberg, Sandra Kiefer, Corto Mascle, Nicolas Waldburger, and Chana Weil-Kennedy. Verification of Population Protocols with Unordered Data. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 156:1-156:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{vanbergerem_et_al:LIPIcs.ICALP.2024.156,
  author =	{van Bergerem, Steffen and Guttenberg, Roland and Kiefer, Sandra and Mascle, Corto and Waldburger, Nicolas and Weil-Kennedy, Chana},
  title =	{{Verification of Population Protocols with Unordered Data}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{156:1--156:20},
  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.2024.156},
  URN =		{urn:nbn:de:0030-drops-202993},
  doi =		{10.4230/LIPIcs.ICALP.2024.156},
  annote =	{Keywords: Population protocols, Parameterized verification, Distributed computing, Well-specification}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.81
A Study of Weisfeiler-Leman Colorings on Planar Graphs

Authors: Sandra Kiefer and Daniel Neuen

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

Abstract
The Weisfeiler-Leman (WL) algorithm is a combinatorial procedure that computes colorings on graphs, which can often be used to detect their (non-)isomorphism. Particularly the 1- and 2-dimensional versions 1-WL and 2-WL have received much attention, due to their numerous links to other areas of computer science. Knowing the expressive power of a certain dimension of the algorithm usually amounts to understanding the computed colorings. An increase in the dimension leads to finer computed colorings and, thus, more graphs can be distinguished. For example, on the class of planar graphs, 3-WL solves the isomorphism problem. However, the expressive power of 2-WL on the class is poorly understood (and, in particular, it may even well be that it decides isomorphism). In this paper, we investigate the colorings computed by 2-WL on planar graphs. Towards this end, we analyze the graphs induced by edge color classes in the graph. Based on the obtained classification, we show that for every 3-connected planar graph, it holds that: a) after coloring all pairs with their 2-WL color, the graph has fixing number 1 with respect to 1-WL, or b) there is a 2-WL-definable matching that can be used to transform the graph into a smaller one, or c) 2-WL detects a connected subgraph that is essentially the graph of a Platonic or Archimedean solid, a prism, a cycle, or a bipartite graph K_{2,𝓁}. In particular, the graphs from case (a) are identified by 2-WL.
Cite as

Sandra Kiefer and Daniel Neuen. A Study of Weisfeiler-Leman Colorings on Planar Graphs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 81:1-81:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kiefer_et_al:LIPIcs.ICALP.2022.81,
  author =	{Kiefer, Sandra and Neuen, Daniel},
  title =	{{A Study of Weisfeiler-Leman Colorings on Planar Graphs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{81:1--81:20},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.81},
  URN =		{urn:nbn:de:0030-drops-164228},
  doi =		{10.4230/LIPIcs.ICALP.2022.81},
  annote =	{Keywords: Weisfeiler-Leman algorithm, planar graphs, edge-transitive graphs, fixing number}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.134
Logarithmic Weisfeiler-Leman Identifies All Planar Graphs

Authors: Martin Grohe and Sandra Kiefer

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

Abstract
The Weisfeiler-Leman (WL) algorithm is a well-known combinatorial procedure for detecting symmetries in graphs and it is widely used in graph-isomorphism tests. It proceeds by iteratively refining a colouring of vertex tuples. The number of iterations needed to obtain the final output is crucial for the parallelisability of the algorithm. We show that there is a constant k such that every planar graph can be identified (that is, distinguished from every non-isomorphic graph) by the k-dimensional WL algorithm within a logarithmic number of iterations. This generalises a result due to Verbitsky (STACS 2007), who proved the same for 3-connected planar graphs. The number of iterations needed by the k-dimensional WL algorithm to identify a graph corresponds to the quantifier depth of a sentence that defines the graph in the (k+1)-variable fragment C^{k+1} of first-order logic with counting quantifiers. Thus, our result implies that every planar graph is definable with a C^{k+1}-sentence of logarithmic quantifier depth.
Cite as

Martin Grohe and Sandra Kiefer. Logarithmic Weisfeiler-Leman Identifies All Planar Graphs. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 134:1-134:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{grohe_et_al:LIPIcs.ICALP.2021.134,
  author =	{Grohe, Martin and Kiefer, Sandra},
  title =	{{Logarithmic Weisfeiler-Leman Identifies All Planar Graphs}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{134:1--134:20},
  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.2021.134},
  URN =		{urn:nbn:de:0030-drops-142035},
  doi =		{10.4230/LIPIcs.ICALP.2021.134},
  annote =	{Keywords: Weisfeiler-Leman algorithm, finite-variable logic, isomorphism testing, planar graphs, quantifier depth, iteration number}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.139
Comparison-Free Polyregular Functions

Authors: Lê Thành Dũng (Tito) Nguyễn, Camille Noûs, and Pierre Pradic

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

Abstract
This paper introduces a new automata-theoretic class of string-to-string functions with polynomial growth. Several equivalent definitions are provided: a machine model which is a restricted variant of pebble transducers, and a few inductive definitions that close the class of regular functions under certain operations. Our motivation for studying this class comes from another characterization, which we merely mention here but prove elsewhere, based on a λ-calculus with a linear type system. As their name suggests, these comparison-free polyregular functions form a subclass of polyregular functions; we prove that the inclusion is strict. We also show that they are incomparable with HDT0L transductions, closed under usual function composition - but not under a certain "map" combinator - and satisfy a comparison-free version of the pebble minimization theorem. On the broader topic of polynomial growth transductions, we also consider the recently introduced layered streaming string transducers (SSTs), or equivalently k-marble transducers. We prove that a function can be obtained by composing such transducers together if and only if it is polyregular, and that k-layered SSTs (or k-marble transducers) are closed under "map" and equivalent to a corresponding notion of (k+1)-layered HDT0L systems.
Cite as

Lê Thành Dũng (Tito) Nguyễn, Camille Noûs, and Pierre Pradic. Comparison-Free Polyregular Functions. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 139:1-139:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{nguyen_et_al:LIPIcs.ICALP.2021.139,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng (Tito) and No\^{u}s, Camille and Pradic, Pierre},
  title =	{{Comparison-Free Polyregular Functions}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{139:1--139:20},
  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.2021.139},
  URN =		{urn:nbn:de:0030-drops-142087},
  doi =		{10.4230/LIPIcs.ICALP.2021.139},
  annote =	{Keywords: pebble transducers, HDT0L systems, polyregular functions}
}
Document
DOI: 10.4230/LIPIcs.CSL.2021.10
Learning Concepts Described By Weight Aggregation Logic

Authors: Steffen van Bergerem and Nicole Schweikardt

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

Abstract
We consider weighted structures, which extend ordinary relational structures by assigning weights, i.e. elements from a particular group or ring, to tuples present in the structure. We introduce an extension of first-order logic that allows to aggregate weights of tuples, compare such aggregates, and use them to build more complex formulas. We provide locality properties of fragments of this logic including Feferman-Vaught decompositions and a Gaifman normal form for a fragment called FOW₁, as well as a localisation theorem for a larger fragment called FOWA₁. This fragment can express concepts from various machine learning scenarios. Using the locality properties, we show that concepts definable in FOWA₁ over a weighted background structure of at most polylogarithmic degree are agnostically PAC-learnable in polylogarithmic time after pseudo-linear time preprocessing.
Cite as

Steffen van Bergerem and Nicole Schweikardt. Learning Concepts Described By Weight Aggregation Logic. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{vanbergerem_et_al:LIPIcs.CSL.2021.10,
  author =	{van Bergerem, Steffen and Schweikardt, Nicole},
  title =	{{Learning Concepts Described By Weight Aggregation Logic}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.10},
  URN =		{urn:nbn:de:0030-drops-134447},
  doi =		{10.4230/LIPIcs.CSL.2021.10},
  annote =	{Keywords: first-order definable concept learning, agnostic probably approximately correct learning, classification problems, locality, Feferman-Vaught decomposition, Gaifman normal form, first-order logic with counting, weight aggregation logic}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.73
The Iteration Number of Colour Refinement

Authors: Sandra Kiefer and Brendan D. McKay

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

Abstract
The Colour Refinement procedure and its generalisation to higher dimensions, the Weisfeiler-Leman algorithm, are central subroutines in approaches to the graph isomorphism problem. In an iterative fashion, Colour Refinement computes a colouring of the vertices of its input graph. A trivial upper bound on the iteration number of Colour Refinement on graphs of order n is n-1. We show that this bound is tight. More precisely, we prove via explicit constructions that there are infinitely many graphs G on which Colour Refinement takes |G|-1 iterations to stabilise. Modifying the infinite families that we present, we show that for every natural number n ≥ 10, there are graphs on n vertices on which Colour Refinement requires at least n-2 iterations to reach stabilisation.
Cite as

Sandra Kiefer and Brendan D. McKay. The Iteration Number of Colour Refinement. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 73:1-73:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kiefer_et_al:LIPIcs.ICALP.2020.73,
  author =	{Kiefer, Sandra and McKay, Brendan D.},
  title =	{{The Iteration Number of Colour Refinement}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{73:1--73:19},
  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.2020.73},
  URN =		{urn:nbn:de:0030-drops-124801},
  doi =		{10.4230/LIPIcs.ICALP.2020.73},
  annote =	{Keywords: Colour Refinement, iteration number, Weisfeiler-Leman algorithm, quantifier depth}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.45
The Power of the Weisfeiler-Leman Algorithm to Decompose Graphs

Authors: Sandra Kiefer and Daniel Neuen

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

Abstract
The Weisfeiler-Leman procedure is a widely-used approach for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, a fundamental tool in structural graph theory, which is often exploited in approaches to tackle the graph isomorphism problem, is the decomposition into bi- and triconnected components. We prove that the 2-dimensional Weisfeiler-Leman algorithm implicitly computes the decomposition of a graph into its triconnected components. Thus, the dimension of the algorithm needed to distinguish two given graphs is at most the dimension required to distinguish the corresponding decompositions into 3-connected components (assuming dimension at least 2). This result implies that for k >= 2, the k-dimensional algorithm distinguishes k-separators, i.e., k-tuples of vertices that separate the graph, from other vertex k-tuples. As a byproduct, we also obtain insights about the connectivity of constituent graphs of association schemes. In an application of the results, we show the new upper bound of k on the Weisfeiler-Leman dimension of graphs of treewidth at most k. Using a construction by Cai, Fürer, and Immerman, we also provide a new lower bound that is asymptotically tight up to a factor of 2.
Cite as

Sandra Kiefer and Daniel Neuen. The Power of the Weisfeiler-Leman Algorithm to Decompose Graphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 45:1-45:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kiefer_et_al:LIPIcs.MFCS.2019.45,
  author =	{Kiefer, Sandra and Neuen, Daniel},
  title =	{{The Power of the Weisfeiler-Leman Algorithm to Decompose Graphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{45:1--45:15},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.45},
  URN =		{urn:nbn:de:0030-drops-109893},
  doi =		{10.4230/LIPIcs.MFCS.2019.45},
  annote =	{Keywords: Weisfeiler-Leman, separators, first-order logic, counting quantifiers}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2019.106
String-to-String Interpretations With Polynomial-Size Output (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Mikołaj Bojańczyk, Sandra Kiefer, and Nathan Lhote

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
String-to-string MSO interpretations are like Courcelle’s MSO transductions, except that a single output position can be represented using a tuple of input positions instead of just a single input position. In particular, the output length is polynomial in the input length, as opposed to MSO transductions, which have output of linear length. We show that string-to-string MSO interpretations are exactly the polyregular functions. The latter class has various characterisations, one of which is that it consists of the string-to-string functions recognised by pebble transducers. Our main result implies the surprising fact that string-to-string MSO interpretations are closed under composition.
Cite as

Mikołaj Bojańczyk, Sandra Kiefer, and Nathan Lhote. String-to-String Interpretations With Polynomial-Size Output (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 106:1-106:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bojanczyk_et_al:LIPIcs.ICALP.2019.106,
  author =	{Boja\'{n}czyk, Miko{\l}aj and Kiefer, Sandra and Lhote, Nathan},
  title =	{{String-to-String Interpretations With Polynomial-Size Output}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{106:1--106:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.106},
  URN =		{urn:nbn:de:0030-drops-106821},
  doi =		{10.4230/LIPIcs.ICALP.2019.106},
  annote =	{Keywords: MSO, interpretations, pebble transducers, polyregular functions}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2019.117
A Linear Upper Bound on the Weisfeiler-Leman Dimension of Graphs of Bounded Genus (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Martin Grohe and Sandra Kiefer

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
The Weisfeiler-Leman (WL) dimension of a graph is a measure for the inherent descriptive complexity of the graph. While originally derived from a combinatorial graph isomorphism test called the Weisfeiler-Leman algorithm, the WL dimension can also be characterised in terms of the number of variables that is required to describe the graph up to isomorphism in first-order logic with counting quantifiers. It is known that the WL dimension is upper-bounded for all graphs that exclude some fixed graph as a minor [M. Grohe, 2017]. However, the bounds that can be derived from this general result are astronomic. Only recently, it was proved that the WL dimension of planar graphs is at most 3 [S. Kiefer et al., 2017]. In this paper, we prove that the WL dimension of graphs embeddable in a surface of Euler genus g is at most 4g+3. For the WL dimension of graphs embeddable in an orientable surface of Euler genus g, our approach yields an upper bound of 2g + 3.
Cite as

Martin Grohe and Sandra Kiefer. A Linear Upper Bound on the Weisfeiler-Leman Dimension of Graphs of Bounded Genus (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 117:1-117:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{grohe_et_al:LIPIcs.ICALP.2019.117,
  author =	{Grohe, Martin and Kiefer, Sandra},
  title =	{{A Linear Upper Bound on the Weisfeiler-Leman Dimension of Graphs of Bounded Genus}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{117:1--117:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.117},
  URN =		{urn:nbn:de:0030-drops-106931},
  doi =		{10.4230/LIPIcs.ICALP.2019.117},
  annote =	{Keywords: Weisfeiler-Leman algorithm, finite-variable logic, isomorphism testing, planar graphs, bounded genus}
}
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