11 Search Results for "Lichter, Moritz"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.18
Supercritical Size-Width Tree-Like Resolution Trade-Offs for Graph Isomorphism

Authors: Christoph Berkholz, Moritz Lichter, and Harry Vinall-Smeeth

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We study the refutation complexity of graph isomorphism in the tree-like resolution calculus. Torán and Wörz [Jacobo Torán and Florian Wörz, 2023] showed that there is a resolution refutation of narrow width k for two graphs if and only if they can be distinguished in (k+1)-variable first-order logic (FO^{k+1}). While DAG-like narrow width k resolution refutations have size at most n^k, tree-like refutations may be much larger. We show that there are graphs of order n, whose isomorphism can be refuted in narrow width k but only in tree-like size 2^{Ω(n^{k/2})}. This is a supercritical trade-off where bounding one parameter (the narrow width) causes the other parameter (the size) to grow above its worst case. The size lower bound is super-exponential in the formula size and improves a related supercritical trade-off by Razborov [Alexander A. Razborov, 2016]. To prove our result, we develop a new variant of the k-pebble EF-game for FO^k to reason about tree-like refutation size in a similar way as the Prover-Delayer games in proof complexity. We analyze this game on the compressed CFI graphs introduced by Grohe, Lichter, Neuen, and Schweitzer [Martin Grohe et al., 2023]. Using a recent improved robust compressed CFI construction of de Rezende, Fleming, Janett, Nordström, and Pang [Susanna F. de Rezende et al., 2024], we obtain a similar bound for width k (instead of the stronger but less common narrow width) and make the result more robust.
Cite as

Christoph Berkholz, Moritz Lichter, and Harry Vinall-Smeeth. Supercritical Size-Width Tree-Like Resolution Trade-Offs for Graph Isomorphism. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{berkholz_et_al:LIPIcs.MFCS.2025.18,
  author =	{Berkholz, Christoph and Lichter, Moritz and Vinall-Smeeth, Harry},
  title =	{{Supercritical Size-Width Tree-Like Resolution Trade-Offs for Graph Isomorphism}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{18:1--18:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.18},
  URN =		{urn:nbn:de:0030-drops-241253},
  doi =		{10.4230/LIPIcs.MFCS.2025.18},
  annote =	{Keywords: Proof complexity, Resolution, Width, Tree-like size, Supercritical trade-off, Lower bound, Finite model theory, CFI graphs}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.24
Super-Critical Trade-Offs in Resolution over Parities via Lifting

Authors: Arkadev Chattopadhyay and Pavel Dvořák

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

Abstract
Razborov [Alexander A. Razborov, 2016] exhibited the following surprisingly strong trade-off phenomenon in propositional proof complexity: for a parameter k = k(n), there exists k-CNF formulas over n variables, having resolution refutations of O(k) width, but every tree-like refutation of width n^{1-ε}/k needs size exp(n^Ω(k)). We extend this result to tree-like Resolution over parities, commonly denoted by Res(⊕), with parameters essentially unchanged. To obtain our result, we extend the lifting theorem of Chattopadhyay, Mande, Sanyal and Sherif [Arkadev Chattopadhyay et al., 2023] to handle tree-like affine DAGs. We introduce additional ideas from linear algebra to handle forget nodes along long paths.
Cite as

Arkadev Chattopadhyay and Pavel Dvořák. Super-Critical Trade-Offs in Resolution over Parities via Lifting. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chattopadhyay_et_al:LIPIcs.CCC.2025.24,
  author =	{Chattopadhyay, Arkadev and Dvo\v{r}\'{a}k, Pavel},
  title =	{{Super-Critical Trade-Offs in Resolution over Parities via Lifting}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{24:1--24:19},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-237186},
  doi =		{10.4230/LIPIcs.CCC.2025.24},
  annote =	{Keywords: Proof complexity, Lifting, Resolution over parities}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.166
Limitations of Affine Integer Relaxations for Solving Constraint Satisfaction Problems

Authors: Moritz Lichter and Benedikt Pago

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We show that various recent algorithms for finite-domain constraint satisfaction problems (CSP), which are based on solving their affine integer relaxations, do not solve all tractable and not even all Maltsev CSPs. This rules them out as candidates for a universal polynomial-time CSP algorithm. The algorithms are ℤ-affine k-consistency, BLP+AIP, BA^{k}, and CLAP. We thereby answer a question by Brakensiek, Guruswami, Wrochna, and Živný [Joshua Brakensiek et al., 2020] whether a constant level of BA^{k}solves all tractable CSPs in the negative: Indeed, not even a sublinear level k suffices. We also refute a conjecture by Dalmau and Opršal [Víctor Dalmau and Jakub Opršal, 2024] (LICS 2024) that every CSP is either solved by ℤ-affine k-consistency or admits a Datalog reduction from 3-colorability. For the cohomological k-consistency algorithm, that is also based on affine relaxations, we show that it correctly solves our counterexample but fails on an NP-complete template.
Cite as

Moritz Lichter and Benedikt Pago. Limitations of Affine Integer Relaxations for Solving Constraint Satisfaction Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 166:1-166:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lichter_et_al:LIPIcs.ICALP.2025.166,
  author =	{Lichter, Moritz and Pago, Benedikt},
  title =	{{Limitations of Affine Integer Relaxations for Solving Constraint Satisfaction Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{166:1--166:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.166},
  URN =		{urn:nbn:de:0030-drops-235431},
  doi =		{10.4230/LIPIcs.ICALP.2025.166},
  annote =	{Keywords: constraint satisfaction, affine relaxation, promise CSPs, \mathbb{Z}-affine k-consistency, cohomological k-consistency algorithm, Tseitin, graph isomorphism}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.129
An Upper Bound on the Weisfeiler-Leman Dimension

Authors: Thomas Schneider and Pascal Schweitzer

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The Weisfeiler-Leman (WL) algorithms form a family of incomplete approaches to the graph isomorphism problem. They recently found various applications in algorithmic group theory and machine learning. In fact, the algorithms form a parameterized family: for each k ∈ ℕ there is a corresponding k-dimensional algorithm WLk. The algorithms become increasingly powerful with increasing dimension, but at the same time the running time increases. The WL-dimension of a graph G is the smallest k ∈ ℕ for which WLk correctly decides isomorphism between G and every other graph. In some sense, the WL-dimension measures how difficult it is to test isomorphism of one graph to others using a fairly general class of combinatorial algorithms. Nowadays, it is a standard measure in descriptive complexity theory for the structural complexity of a graph. We prove that the WL-dimension of a graph on n vertices is at most 3/20 ⋅ n + o(n) = 0.15 ⋅ n + o(n). Reducing the question to coherent configurations, the proof develops various techniques to analyze their structure. This includes sufficient conditions under which a fiber can be restored uniquely up to isomorphism if it is removed, a recursive proof exploiting a degree reduction and treewidth bounds, as well as an exhaustive analysis of interspaces involving small fibers. As a base case, we also analyze the dimension of coherent configurations with small fiber size and thereby graphs with small color class size.
Cite as

Thomas Schneider and Pascal Schweitzer. An Upper Bound on the Weisfeiler-Leman Dimension. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 129:1-129:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{schneider_et_al:LIPIcs.ICALP.2025.129,
  author =	{Schneider, Thomas and Schweitzer, Pascal},
  title =	{{An Upper Bound on the Weisfeiler-Leman Dimension}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{129:1--129:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.129},
  URN =		{urn:nbn:de:0030-drops-235065},
  doi =		{10.4230/LIPIcs.ICALP.2025.129},
  annote =	{Keywords: Weisfeiler-Leman dimension, descriptive complexity, coherent configurations}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.13
Computational Complexity of the Weisfeiler-Leman Dimension

Authors: Moritz Lichter, Simon Raßmann, and Pascal Schweitzer

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
The Weisfeiler-Leman dimension of a graph G is the least number k such that the k-dimensional Weisfeiler-Leman algorithm distinguishes G from every other non-isomorphic graph, or equivalently, the least k such that G is definable in (k+1)-variable first-order logic with counting. The dimension is a standard measure of the descriptive or structural complexity of a graph and recently finds various applications in particular in the context of machine learning. This paper studies the complexity of computing the Weisfeiler-Leman dimension. We observe that deciding whether the Weisfeiler-Leman dimension of G is at most k is NP-hard, even if G is restricted to have 4-bounded color classes. For each fixed k ≥ 2, we give a polynomial-time algorithm that decides whether the Weisfeiler-Leman dimension of a given graph with 5-bounded color classes is at most k. Moreover, we show that for these bounds on the color classes, this is optimal because the problem is PTIME-hard under logspace-uniform AC_0-reductions. Furthermore, for each larger bound c on the color classes and each fixed k ≥ 2, we provide a polynomial-time decision algorithm for the abelian case, that is, for structures of which each color class has an abelian automorphism group. While the graph classes we consider may seem quite restrictive, graphs with 4-bounded abelian colors include CFI-graphs and multipedes, which form the basis of almost all known hard instances and lower bounds related to the Weisfeiler-Leman algorithm.
Cite as

Moritz Lichter, Simon Raßmann, and Pascal Schweitzer. Computational Complexity of the Weisfeiler-Leman Dimension. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lichter_et_al:LIPIcs.CSL.2025.13,
  author =	{Lichter, Moritz and Ra{\ss}mann, Simon and Schweitzer, Pascal},
  title =	{{Computational Complexity of the Weisfeiler-Leman Dimension}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{13:1--13:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.13},
  URN =		{urn:nbn:de:0030-drops-227707},
  doi =		{10.4230/LIPIcs.CSL.2025.13},
  annote =	{Keywords: Weisfeiler-Leman algorithm, dimension, complexity, coherent configurations}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.14
Finite Variable Counting Logics with Restricted Requantification

Authors: Simon Raßmann, Georg Schindling, and Pascal Schweitzer

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Counting logics with a bounded number of variables form one of the central concepts in descriptive complexity theory. Although they restrict the number of variables that a formula can contain, the variables can be nested within scopes of quantified occurrences of themselves. In other words, the variables can be requantified. We study the fragments obtained from counting logics by restricting requantification for some but not necessarily all the variables. Similar to the logics without limitation on requantification, we develop tools to investigate the restricted variants. Specifically, we introduce a bijective pebble game in which certain pebbles can only be placed once and for all, and a corresponding two-parametric family of Weisfeiler-Leman algorithms. We show close correspondences between the three concepts. By using a suitable cops-and-robber game and adaptations of the Cai-Fürer-Immerman construction, we completely clarify the relative expressive power of the new logics. We show that the restriction of requantification has beneficial algorithmic implications in terms of graph identification. Indeed, we argue that with regard to space complexity, non-requantifiable variables only incur an additive polynomial factor when testing for equivalence. In contrast, for all we know, requantifiable variables incur a multiplicative linear factor. Finally, we observe that graphs of bounded tree-depth and 3-connected planar graphs can be identified using no, respectively, only a very limited number of requantifiable variables.
Cite as

Simon Raßmann, Georg Schindling, and Pascal Schweitzer. Finite Variable Counting Logics with Restricted Requantification. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{ramann_et_al:LIPIcs.CSL.2025.14,
  author =	{Ra{\ss}mann, Simon and Schindling, Georg and Schweitzer, Pascal},
  title =	{{Finite Variable Counting Logics with Restricted Requantification}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{14:1--14:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.14},
  URN =		{urn:nbn:de:0030-drops-227716},
  doi =		{10.4230/LIPIcs.CSL.2025.14},
  annote =	{Keywords: Requantification, Finite variable counting logics, Weisfeiler-Leman algorithm}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.36
Limitations of Game Comonads for Invertible-Map Equivalence via Homomorphism Indistinguishability

Authors: Moritz Lichter, Benedikt Pago, and Tim Seppelt

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
Abramsky, Dawar, and Wang (2017) introduced the pebbling comonad for k-variable counting logic and thereby initiated a line of work that imports category theoretic machinery to finite model theory. Such game comonads have been developed for various logics, yielding characterisations of logical equivalences in terms of isomorphisms in the associated co-Kleisli category. We show a first limitation of this approach by studying linear-algebraic logic, which is strictly more expressive than first-order counting logic and whose k-variable logical equivalence relations are known as invertible-map equivalences (IM). We show that there exists no finite-rank comonad on the category of graphs whose co-Kleisli isomorphisms characterise IM-equivalence, answering a question of Ó Conghaile and Dawar (CSL 2021). We obtain this result by ruling out a characterisation of IM-equivalence in terms of homomorphism indistinguishability and employing the Lovász-type theorem for game comonads established by Reggio (2022). Two graphs are homomorphism indistinguishable over a graph class if they admit the same number of homomorphisms from every graph in the class. The IM-equivalences cannot be characterised in this way, neither when counting homomorphisms in the natural numbers, nor in any finite prime field.
Cite as

Moritz Lichter, Benedikt Pago, and Tim Seppelt. Limitations of Game Comonads for Invertible-Map Equivalence via Homomorphism Indistinguishability. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{lichter_et_al:LIPIcs.CSL.2024.36,
  author =	{Lichter, Moritz and Pago, Benedikt and Seppelt, Tim},
  title =	{{Limitations of Game Comonads for Invertible-Map Equivalence via Homomorphism Indistinguishability}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{36:1--36:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.36},
  URN =		{urn:nbn:de:0030-drops-196799},
  doi =		{10.4230/LIPIcs.CSL.2024.36},
  annote =	{Keywords: finite model theory, graph isomorphism, linear-algebraic logic, homomorphism indistinguishability, game comonads, invertible-map equivalence}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.133
Witnessed Symmetric Choice and Interpretations in Fixed-Point Logic with Counting

Authors: Moritz Lichter

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
At the core of the quest for a logic for Ptime is a mismatch between algorithms making arbitrary choices and isomorphism-invariant logics. One approach to tackle this problem is witnessed symmetric choice. It allows for choices from definable orbits certified by definable witnessing automorphisms. We consider the extension of fixed-point logic with counting (IFPC) with witnessed symmetric choice (IFPC+WSC) and a further extension with an interpretation operator (IFPC+WSC+I). The latter operator evaluates a subformula in the structure defined by an interpretation. When similarly extending pure fixed-point logic (IFP), IFP+WSC+I simulates counting which IFP+WSC fails to do. For IFPC+WSC, it is unknown whether the interpretation operator increases expressiveness and thus allows studying the relation between WSC and interpretations beyond counting. In this paper, we separate IFPC+WSC from IFPC+WSC+I by showing that IFPC+WSC is not closed under FO-interpretations. By the same argument, we answer an open question of Dawar and Richerby regarding non-witnessed symmetric choice in IFP. Additionally, we prove that nesting WSC-operators increases the expressiveness using the so-called CFI graphs. We show that if IFPC+WSC+I canonizes a particular class of base graphs, then it also canonizes the corresponding CFI graphs. This differs from various other logics, where CFI graphs provide difficult instances.
Cite as

Moritz Lichter. Witnessed Symmetric Choice and Interpretations in Fixed-Point Logic with Counting. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 133:1-133:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{lichter:LIPIcs.ICALP.2023.133,
  author =	{Lichter, Moritz},
  title =	{{Witnessed Symmetric Choice and Interpretations in Fixed-Point Logic with Counting}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{133:1--133:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.133},
  URN =		{urn:nbn:de:0030-drops-181858},
  doi =		{10.4230/LIPIcs.ICALP.2023.133},
  annote =	{Keywords: witnessed symmetric choice, interpretation, fixed-point logic, counting, CFI graphs, logic for PTime}
}
Document
DOI: 10.4230/LIPIcs.SAT.2022.1
SAT Preprocessors and Symmetry

Authors: Markus Anders

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)

Abstract
Exploitation of symmetries is an indispensable approach to solve certain classes of difficult SAT instances. Numerous techniques for the use of symmetry in SAT have evolved over the past few decades. But no matter how symmetries are used precisely, they have to be detected first. We investigate how to detect more symmetry, faster. The initial idea is to reap the benefits of SAT preprocessing for symmetry detection. As it turns out, applying an off-the-shelf preprocessor before handling symmetry runs into problems: the preprocessor can haphazardly remove symmetry from formulas, severely impeding symmetry exploitation. Our main contribution is a theoretical framework that captures the relationship of SAT preprocessing techniques and symmetry. Based on this, we create a symmetry-aware preprocessor that can be applied safely before handling symmetry. We then demonstrate that applying the preprocessor does not only substantially decrease symmetry detection and breaking times, but also uncovers hidden symmetry not detectable in the original instances. Overall, we depart the conventional view of treating symmetry detection as a black-box, presenting a new application-specific approach to symmetry detection in SAT.
Cite as

Markus Anders. SAT Preprocessors and Symmetry. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{anders:LIPIcs.SAT.2022.1,
  author =	{Anders, Markus},
  title =	{{SAT Preprocessors and Symmetry}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.1},
  URN =		{urn:nbn:de:0030-drops-166752},
  doi =		{10.4230/LIPIcs.SAT.2022.1},
  annote =	{Keywords: boolean satisfiability, symmetry exploitation, graph isomorphism}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.6
Parallel Computation of Combinatorial Symmetries

Authors: Markus Anders and Pascal Schweitzer

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the automorphism group of the constructed graph. Such solvers have been developed for over 50 years, and highly efficient sequential, single core tools are available. However no competitive parallel tools are available for the task. We introduce a new parallel randomized algorithm that is based on a modification of the individualization-refinement paradigm used by sequential solvers. The use of randomization crucially enables parallelization. We report extensive benchmark results that show that our solver is competitive to state-of-the-art solvers on a single thread, while scaling remarkably well with the use of more threads. This results in order-of-magnitude improvements on many graph classes over state-of-the-art solvers. In fact, our tool is the first parallel graph automorphism tool that outperforms current sequential tools.
Cite as

Markus Anders and Pascal Schweitzer. Parallel Computation of Combinatorial Symmetries. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{anders_et_al:LIPIcs.ESA.2021.6,
  author =	{Anders, Markus and Schweitzer, Pascal},
  title =	{{Parallel Computation of Combinatorial Symmetries}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.6},
  URN =		{urn:nbn:de:0030-drops-145875},
  doi =		{10.4230/LIPIcs.ESA.2021.6},
  annote =	{Keywords: graph isomorphism, automorphism groups, algorithm engineering, parallel algorithms}
}
Document
DOI: 10.4230/LIPIcs.CSL.2021.31
Canonization for Bounded and Dihedral Color Classes in Choiceless Polynomial Time

Authors: Moritz Lichter and Pascal Schweitzer

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

Abstract
In the quest for a logic capturing Ptime the next natural classes of structures to consider are those with bounded color class size. We present a canonization procedure for graphs with dihedral color classes of bounded size in the logic of Choiceless Polynomial Time (CPT), which then captures Ptime on this class of structures. This is the first result of this form for non-abelian color classes. The first step proposes a normal form which comprises a "rigid assemblage". This roughly means that the local automorphism groups form 2-injective 3-factor subdirect products. Structures with color classes of bounded size can be reduced canonization preservingly to normal form in CPT. In the second step, we show that for graphs in normal form with dihedral color classes of bounded size, the canonization problem can be solved in CPT. We also show the same statement for general ternary structures in normal form if the dihedral groups are defined over odd domains.
Cite as

Moritz Lichter and Pascal Schweitzer. Canonization for Bounded and Dihedral Color Classes in Choiceless Polynomial Time. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 31:1-31:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{lichter_et_al:LIPIcs.CSL.2021.31,
  author =	{Lichter, Moritz and Schweitzer, Pascal},
  title =	{{Canonization for Bounded and Dihedral Color Classes in Choiceless Polynomial Time}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{31:1--31:18},
  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.2021.31},
  URN =		{urn:nbn:de:0030-drops-134650},
  doi =		{10.4230/LIPIcs.CSL.2021.31},
  annote =	{Keywords: Choiceless polynomial time, canonization, relational structures, bounded color class size, dihedral groups}
}
  • Refine by Type
  • 11 Document/PDF
  • 6 Document/HTML

  • Refine by Publication Year
  • 6 2025
  • 1 2024
  • 1 2023
  • 1 2022
  • 2 2021

  • Refine by Author
  • 6 Lichter, Moritz
  • 5 Schweitzer, Pascal
  • 2 Anders, Markus
  • 2 Pago, Benedikt
  • 2 Raßmann, Simon
  • Show More...

  • Refine by Series/Journal
  • 11 LIPIcs

  • Refine by Classification
  • 6 Theory of computation → Complexity theory and logic
  • 5 Theory of computation → Finite Model Theory
  • 3 Mathematics of computing → Graph algorithms
  • 3 Theory of computation → Problems, reductions and completeness
  • 2 Theory of computation → Graph algorithms analysis
  • Show More...

  • Refine by Keyword
  • 4 graph isomorphism
  • 2 CFI graphs
  • 2 Proof complexity
  • 2 Weisfeiler-Leman algorithm
  • 2 coherent configurations
  • 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