86 Search Results for "J�z�quel, Jean-Marc"

Document
DOI: 10.4230/LIPIcs.CSL.2024.21
Reverse Tangent Categories

Authors: Geoffrey Cruttwell and Jean-Simon Pacaud Lemay

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

Abstract
Previous work has shown that reverse differential categories give an abstract setting for gradient-based learning of functions between Euclidean spaces. However, reverse differential categories are not suited to handle gradient-based learning for functions between more general spaces such as smooth manifolds. In this paper, we propose a setting to handle this, which we call reverse tangent categories: tangent categories with an involution operation for their differential bundles.
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Geoffrey Cruttwell and Jean-Simon Pacaud Lemay. Reverse Tangent Categories. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 21:1-21:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cruttwell_et_al:LIPIcs.CSL.2024.21,
  author =	{Cruttwell, Geoffrey and Lemay, Jean-Simon Pacaud},
  title =	{{Reverse Tangent Categories}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{21:1--21:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.21},
  URN =		{urn:nbn:de:0030-drops-196644},
  doi =		{10.4230/LIPIcs.CSL.2024.21},
  annote =	{Keywords: Tangent Categories, Reverse Tangent Categories, Reverse Differential Categories, Categorical Machine Learning}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.28
Realizability Models for Large Cardinals

Authors: Laura Fontanella, Guillaume Geoffroy, and Richard Matthews

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

Abstract
Realizabilty is a branch of logic that aims at extracting the computational content of mathematical proofs by establishing a correspondence between proofs and programs. Invented by S.C. Kleene in the 1945 to develop a connection between intuitionism and Turing computable functions, realizability has evolved to include not only classical logic but even set theory, thanks to the work of J-L. Krivine. Krivine’s work made possible to build realizability models for Zermelo-Frænkel set theory, ZF, assuming its consistency. Nevertheless, a large part of set theoretic research involves investigating further axioms that are known as large cardinals axioms; in this paper we focus on four large cardinals axioms: the axioms of (strongly) inaccessible cardinal, Mahlo cardinals, measurable cardinals and Reinhardt cardinals. We show how to build realizability models for each of these four axioms assuming their consistency relative to ZFC or ZF.
Cite as

Laura Fontanella, Guillaume Geoffroy, and Richard Matthews. Realizability Models for Large Cardinals. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fontanella_et_al:LIPIcs.CSL.2024.28,
  author =	{Fontanella, Laura and Geoffroy, Guillaume and Matthews, Richard},
  title =	{{Realizability Models for Large Cardinals}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{28:1--28:18},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.28},
  URN =		{urn:nbn:de:0030-drops-196715},
  doi =		{10.4230/LIPIcs.CSL.2024.28},
  annote =	{Keywords: Logic, Classical Realizability, Set Theory, Large Cardinals}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.29
Constraint Automata on Infinite Data Trees: from CTL(ℤ)/CTL^*(ℤ) to Decision Procedures

Authors: Stéphane Demri and Karin Quaas

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
We introduce the class of tree constraint automata with data values in ℤ (equipped with the less than relation and equality predicates to constants), and we show that the nonemptiness problem is EXPTIME-complete. Using an automata-based approach, we establish that the satisfiability problem for CTL(ℤ) (CTL with constraints in ℤ) is EXPTIME-complete, and the satisfiability problem for CTL^*(ℤ) is 2ExpTime-complete (only decidability was known so far). By-product results with other concrete domains and other logics, are also briefly discussed.
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Stéphane Demri and Karin Quaas. Constraint Automata on Infinite Data Trees: from CTL(ℤ)/CTL^*(ℤ) to Decision Procedures. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{demri_et_al:LIPIcs.CONCUR.2023.29,
  author =	{Demri, St\'{e}phane and Quaas, Karin},
  title =	{{Constraint Automata on Infinite Data Trees: from CTL(\mathbb{Z})/CTL^*(\mathbb{Z}) to Decision Procedures}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.29},
  URN =		{urn:nbn:de:0030-drops-190238},
  doi =		{10.4230/LIPIcs.CONCUR.2023.29},
  annote =	{Keywords: Constraints, Constraint Automata, Temporal Logics, Infinite Data Trees}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.36
The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets

Authors: Petr Jančar and Jérôme Leroux

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
A set of configurations H is a home-space for a set of configurations X of a Petri net if every configuration reachable from (any configuration in) X can reach (some configuration in) H. The semilinear home-space problem for Petri nets asks, given a Petri net and semilinear sets of configurations X, H, if H is a home-space for X. In 1989, David de Frutos Escrig and Colette Johnen proved that the problem is decidable when X is a singleton and H is a finite union of linear sets with the same periods. In this paper, we show that the general (semilinear) problem is decidable. This result is obtained by proving a duality between the reachability problem and the non-home-space problem. In particular, we prove that for any Petri net and any linear set of configurations L we can effectively compute a semilinear set C of configurations, called a non-reachability core for L, such that for every set X the set L is not a home-space for X if, and only if, C is reachable from X. We show that the established relation to the reachability problem yields the Ackermann-completeness of the (semilinear) home-space problem. For this we also show that, given a Petri net with an initial marking, the set of minimal reachable markings can be constructed in Ackermannian time.
Cite as

Petr Jančar and Jérôme Leroux. The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jancar_et_al:LIPIcs.CONCUR.2023.36,
  author =	{Jan\v{c}ar, Petr and Leroux, J\'{e}r\^{o}me},
  title =	{{The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.36},
  URN =		{urn:nbn:de:0030-drops-190300},
  doi =		{10.4230/LIPIcs.CONCUR.2023.36},
  annote =	{Keywords: Petri nets, home-space property, semilinear sets, Ackermannian complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.26
Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games

Authors: Léonard Brice, Jean-François Raskin, and Marie van den Bogaard

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

Abstract
We study a natural problem about rational behaviors in multiplayer non-zero-sum sequential infinite duration games played on graphs: rational verification, that consists in deciding whether all the rational answers to a given strategy satisfy some specification. We give the complexities of that problem for two major concepts of rationality: Nash equilibria and subgame-perfect equilibria, and for three major classes of payoff functions: energy, discounted-sum, and mean-payoff.
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Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{brice_et_al:LIPIcs.MFCS.2023.26,
  author =	{Brice, L\'{e}onard and Raskin, Jean-Fran\c{c}ois and van den Bogaard, Marie},
  title =	{{Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{26:1--26:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.26},
  URN =		{urn:nbn:de:0030-drops-185608},
  doi =		{10.4230/LIPIcs.MFCS.2023.26},
  annote =	{Keywords: Games on graphs, Nash equilibria, subgame-perfect equilibria}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.56
Pursuit-Evasion in Graphs: Zombies, Lazy Zombies and a Survivor

Authors: Prosenjit Bose, Jean-Lou De Carufel, and Thomas Shermer

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We study zombies and survivor, a variant of the game of cops and robber on graphs. In this variant, the single survivor plays the role of the robber and attempts to escape from the zombies that play the role of the cops. The zombies are restricted, on their turn, to always follow an edge of a shortest path towards the survivor. Let z(G) be the smallest number of zombies required to catch the survivor on a graph G with n vertices. We show that there exist outerplanar graphs and visibility graphs of simple polygons such that z(G) = Θ(n). We also show that there exist maximum-degree-3 outerplanar graphs such that z(G) = Ω(n/log(n)). Let z_L(G) be the smallest number of lazy zombies (zombies that can stay still on their turn) required to catch the survivor on a graph G. We show that lazy zombies are more powerful than normal zombies but less powerful than cops. We prove that z_L(G) ≤ 2 for connected outerplanar graphs and this bound is tight in the worst case. We show that z_L(G) ≤ k for connected graphs with treedepth k. This result implies that z_L(G) is at most (k+1)log n for connected graphs with treewidth k, O(√n) for connected planar graphs, O(√{gn}) for connected graphs with genus g and O(h√{hn}) for connected graphs with any excluded h-vertex minor. Our results on lazy zombies still hold when an adversary chooses the initial positions of the zombies.
Cite as

Prosenjit Bose, Jean-Lou De Carufel, and Thomas Shermer. Pursuit-Evasion in Graphs: Zombies, Lazy Zombies and a Survivor. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 56:1-56:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bose_et_al:LIPIcs.ISAAC.2022.56,
  author =	{Bose, Prosenjit and De Carufel, Jean-Lou and Shermer, Thomas},
  title =	{{Pursuit-Evasion in Graphs: Zombies, Lazy Zombies and a Survivor}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{56:1--56:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.56},
  URN =		{urn:nbn:de:0030-drops-173418},
  doi =		{10.4230/LIPIcs.ISAAC.2022.56},
  annote =	{Keywords: Pursuit-evasion games, Outerplanar, Graphs, Treedepth, Treewidth}
}
Document
DOI: 10.4230/DagRep.12.1.1
Mobility Data Science (Dagstuhl Seminar 22021)

Authors: Mohamed Mokbel, Mahmoud Sakr, Li Xiong, Andreas Züfle, Jussara Almeida, Taylor Anderson, Walid Aref, Gennady Andrienko, Natalia Andrienko, Yang Cao, Sanjay Chawla, Reynold Cheng, Panos Chrysanthis, Xiqi Fei, Gabriel Ghinita, Anita Graser, Dimitrios Gunopulos, Christian Jensen, Joon-Sook Kim, Kyoung-Sook Kim, Peer Kröger, John Krumm, Johannes Lauer, Amr Magdy, Mario Nascimento, Siva Ravada, Matthias Renz, Dimitris Sacharidis, Cyrus Shahabi, Flora Salim, Mohamed Sarwat, Maxime Schoemans, Bettina Speckmann, Egemen Tanin, Yannis Theodoridis, Kristian Torp, Goce Trajcevski, Marc van Kreveld, Carola Wenk, Martin Werner, Raymond Wong, Song Wu, Jianqiu Xu, Moustafa Youssef, Demetris Zeinalipour, Mengxuan Zhang, and Esteban Zimányi

Published in: Dagstuhl Reports, Volume 12, Issue 1 (2022)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 22021 "Mobility Data Science". This seminar was held January 9-14, 2022, including 47 participants from industry and academia. The goal of this Dagstuhl Seminar was to create a new research community of mobility data science in which the whole is greater than the sum of its parts by bringing together established leaders as well as promising young researchers from all fields related to mobility data science. Specifically, this report summarizes the main results of the seminar by (1) defining Mobility Data Science as a research domain, (2) by sketching its agenda in the coming years, and by (3) building a mobility data science community. (1) Mobility data science is defined as spatiotemporal data that additionally captures the behavior of moving entities (human, vehicle, animal, etc.). To understand, explain, and predict behavior, we note that a strong collaboration with research in behavioral and social sciences is needed. (2) Future research directions for mobility data science described in this report include a) mobility data acquisition and privacy, b) mobility data management and analysis, and c) applications of mobility data science. (3) We identify opportunities towards building a mobility data science community, towards collaborations between academic and industry, and towards a mobility data science curriculum.
Cite as

Mohamed Mokbel, Mahmoud Sakr, Li Xiong, Andreas Züfle, Jussara Almeida, Taylor Anderson, Walid Aref, Gennady Andrienko, Natalia Andrienko, Yang Cao, Sanjay Chawla, Reynold Cheng, Panos Chrysanthis, Xiqi Fei, Gabriel Ghinita, Anita Graser, Dimitrios Gunopulos, Christian Jensen, Joon-Sook Kim, Kyoung-Sook Kim, Peer Kröger, John Krumm, Johannes Lauer, Amr Magdy, Mario Nascimento, Siva Ravada, Matthias Renz, Dimitris Sacharidis, Cyrus Shahabi, Flora Salim, Mohamed Sarwat, Maxime Schoemans, Bettina Speckmann, Egemen Tanin, Yannis Theodoridis, Kristian Torp, Goce Trajcevski, Marc van Kreveld, Carola Wenk, Martin Werner, Raymond Wong, Song Wu, Jianqiu Xu, Moustafa Youssef, Demetris Zeinalipour, Mengxuan Zhang, and Esteban Zimányi. Mobility Data Science (Dagstuhl Seminar 22021). In Dagstuhl Reports, Volume 12, Issue 1, pp. 1-34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{mokbel_et_al:DagRep.12.1.1,
  author =	{Mokbel, Mohamed and Sakr, Mahmoud and Xiong, Li and Z\"{u}fle, Andreas and Almeida, Jussara and Anderson, Taylor and Aref, Walid and Andrienko, Gennady and Andrienko, Natalia and Cao, Yang and Chawla, Sanjay and Cheng, Reynold and Chrysanthis, Panos and Fei, Xiqi and Ghinita, Gabriel and Graser, Anita and Gunopulos, Dimitrios and Jensen, Christian and Kim, Joon-Sook and Kim, Kyoung-Sook and Kr\"{o}ger, Peer and Krumm, John and Lauer, Johannes and Magdy, Amr and Nascimento, Mario and Ravada, Siva and Renz, Matthias and Sacharidis, Dimitris and Shahabi, Cyrus and Salim, Flora and Sarwat, Mohamed and Schoemans, Maxime and Speckmann, Bettina and Tanin, Egemen and Theodoridis, Yannis and Torp, Kristian and Trajcevski, Goce and van Kreveld, Marc and Wenk, Carola and Werner, Martin and Wong, Raymond and Wu, Song and Xu, Jianqiu and Youssef, Moustafa and Zeinalipour, Demetris and Zhang, Mengxuan and Zim\'{a}nyi, Esteban},
  title =	{{Mobility Data Science (Dagstuhl Seminar 22021)}},
  pages =	{1--34},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{12},
  number =	{1},
  editor =	{Mokbel, Mohamed and Sakr, Mahmoud and Xiong, Li and Z\"{u}fle, Andreas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.12.1.1},
  URN =		{urn:nbn:de:0030-drops-169190},
  doi =		{10.4230/DagRep.12.1.1},
  annote =	{Keywords: Spatio-temporal, Tracking, Privacy, Behavior, Data cleaning, Data management, Analytics}
}
Document
DOI: 10.4230/LIPIcs.SAT.2022.28
A New Exact Solver for (Weighted) Max#SAT

Authors: Gilles Audemard, Jean-Marie Lagniez, and Marie Miceli

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

Abstract
We present and evaluate d4Max, an exact approach for solving the Weighted Max#SAT problem. The Max#SAT problem extends the model counting problem (#SAT) by considering a tripartition of the variables {X, Y, Z}, and consists in maximizing over X the number of assignments to Y that can be extended to a solution with some assignment to Z. The Weighted Max#SAT problem is an extension of the Max#SAT problem with weights associated on each interpretation. We test and compare our approach with other state-of-the-art solvers on the challenging task in probabilistic inference of finding the marginal maximum a posteriori probability (MMAP) of a given subset of the variables in a Bayesian network and on exist-random quantified SSAT benchmarks. The results clearly show the overall superiority of d4Max in term of speed and number of instances solved. Moreover, we experimentally show that, in general, d4Max is able to quickly spot a solution that is close to optimal, thereby opening the door to an efficient anytime approach.
Cite as

Gilles Audemard, Jean-Marie Lagniez, and Marie Miceli. A New Exact Solver for (Weighted) Max#SAT. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{audemard_et_al:LIPIcs.SAT.2022.28,
  author =	{Audemard, Gilles and Lagniez, Jean-Marie and Miceli, Marie},
  title =	{{A New Exact Solver for (Weighted) Max#SAT}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{28:1--28:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.28},
  URN =		{urn:nbn:de:0030-drops-167022},
  doi =		{10.4230/LIPIcs.SAT.2022.28},
  annote =	{Keywords: Max#SAT, EMaj-SAT, Weighted Projected Model Counting, SSAT}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.3
Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model

Authors: Boris Aronov, Mark de Berg, Jean Cardinal, Esther Ezra, John Iacono, and Micha Sharir

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We present subquadratic algorithms in the algebraic decision-tree model for several 3Sum-hard geometric problems, all of which can be reduced to the following question: Given two sets A, B, each consisting of n pairwise disjoint segments in the plane, and a set C of n triangles in the plane, we want to count, for each triangle Δ ∈ C, the number of intersection points between the segments of A and those of B that lie in Δ. The problems considered in this paper have been studied by Chan (2020), who gave algorithms that solve them, in the standard real-RAM model, in O((n²/log²n) log^O(1) log n) time. We present solutions in the algebraic decision-tree model whose cost is O(n^{60/31+ε}), for any ε > 0. Our approach is based on a primal-dual range searching mechanism, which exploits the multi-level polynomial partitioning machinery recently developed by Agarwal, Aronov, Ezra, and Zahl (2020). A key step in the procedure is a variant of point location in arrangements, say of lines in the plane, which is based solely on the order type of the lines, a "handicap" that turns out to be beneficial for speeding up our algorithm.
Cite as

Boris Aronov, Mark de Berg, Jean Cardinal, Esther Ezra, John Iacono, and Micha Sharir. Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{aronov_et_al:LIPIcs.ISAAC.2021.3,
  author =	{Aronov, Boris and de Berg, Mark and Cardinal, Jean and Ezra, Esther and Iacono, John and Sharir, Micha},
  title =	{{Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.3},
  URN =		{urn:nbn:de:0030-drops-154363},
  doi =		{10.4230/LIPIcs.ISAAC.2021.3},
  annote =	{Keywords: Computational geometry, Algebraic decision-tree model, Polynomial partitioning, Primal-dual range searching, Order types, Point location, Hierarchical partitions}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.49
Keyboards as a New Model of Computation

Authors: Yoan Géran, Bastien Laboureix, Corto Mascle, and Valentin D. Richard

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We introduce a new formalisation of language computation, called keyboards. We consider a set of atomic operations (writing a letter, erasing a letter, going to the right or to the left) and we define a keyboard as a set of finite sequences of such operations, called keys. The generated language is the set of words obtained by applying some non-empty sequence of those keys. Unlike classical models of computation, every key can be applied anytime. We define various classes of languages based on different sets of atomic operations, and compare their expressive powers. We also compare them to rational, context-free and context-sensitive languages. We obtain a strict hierarchy of classes, whose expressiveness is orthogonal to the one of the aforementioned classical models. We also study closure properties of those classes, as well as fundamental complexity problems on keyboards.
Cite as

Yoan Géran, Bastien Laboureix, Corto Mascle, and Valentin D. Richard. Keyboards as a New Model of Computation. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 49:1-49:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{geran_et_al:LIPIcs.MFCS.2021.49,
  author =	{G\'{e}ran, Yoan and Laboureix, Bastien and Mascle, Corto and Richard, Valentin D.},
  title =	{{Keyboards as a New Model of Computation}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{49:1--49:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.49},
  URN =		{urn:nbn:de:0030-drops-144896},
  doi =		{10.4230/LIPIcs.MFCS.2021.49},
  annote =	{Keywords: formal languages, models of computation, automata theory}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.51
A Note on the Join of Varieties of Monoids with LI

Authors: Nathan Grosshans

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
In this note, we give a characterisation in terms of identities of the join of V with the variety of finite locally trivial semigroups LI for several well-known varieties of finite monoids V by using classical algebraic-automata-theoretic techniques. To achieve this, we use the new notion of essentially-V stamps defined by Grosshans, McKenzie and Segoufin and show that it actually coincides with the join of V and LI precisely when some natural condition on the variety of languages corresponding to V is verified. This work is a kind of rediscovery of the work of J. C. Costa around 20 years ago from a rather different angle, since Costa’s work relies on the use of advanced developments in profinite topology, whereas what is presented here essentially uses an algebraic, language-based approach.
Cite as

Nathan Grosshans. A Note on the Join of Varieties of Monoids with LI. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 51:1-51:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{grosshans:LIPIcs.MFCS.2021.51,
  author =	{Grosshans, Nathan},
  title =	{{A Note on the Join of Varieties of Monoids with LI}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{51:1--51:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.51},
  URN =		{urn:nbn:de:0030-drops-144918},
  doi =		{10.4230/LIPIcs.MFCS.2021.51},
  annote =	{Keywords: Varieties of monoids, join, LI}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.84
Parameterized (Modular) Counting and Cayley Graph Expanders

Authors: Norbert Peyerimhoff, Marc Roth, Johannes Schmitt, Jakob Stix, and Alina Vdovina

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We study the problem #EdgeSub(Φ) of counting k-edge subgraphs satisfying a given graph property Φ in a large host graph G. Building upon the breakthrough result of Curticapean, Dell and Marx (STOC 17), we express the number of such subgraphs as a finite linear combination of graph homomorphism counts and derive the complexity of computing this number by studying its coefficients. Our approach relies on novel constructions of low-degree Cayley graph expanders of p-groups, which might be of independent interest. The properties of those expanders allow us to analyse the coefficients in the aforementioned linear combinations over the field 𝔽_p which gives us significantly more control over the cancellation behaviour of the coefficients. Our main result is an exhaustive and fine-grained complexity classification of #EdgeSub(Φ) for minor-closed properties Φ, closing the missing gap in previous work by Roth, Schmitt and Wellnitz (ICALP 21). Additionally, we observe that our methods also apply to modular counting. Among others, we obtain novel intractability results for the problems of counting k-forests and matroid bases modulo a prime p. Furthermore, from an algorithmic point of view, we construct algorithms for the problems of counting k-paths and k-cycles modulo 2 that outperform the best known algorithms for their non-modular counterparts. In the course of our investigations we also provide an exhaustive parameterized complexity classification for the problem of counting graph homomorphisms modulo a prime p.
Cite as

Norbert Peyerimhoff, Marc Roth, Johannes Schmitt, Jakob Stix, and Alina Vdovina. Parameterized (Modular) Counting and Cayley Graph Expanders. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 84:1-84:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{peyerimhoff_et_al:LIPIcs.MFCS.2021.84,
  author =	{Peyerimhoff, Norbert and Roth, Marc and Schmitt, Johannes and Stix, Jakob and Vdovina, Alina},
  title =	{{Parameterized (Modular) Counting and Cayley Graph Expanders}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{84:1--84:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.84},
  URN =		{urn:nbn:de:0030-drops-145246},
  doi =		{10.4230/LIPIcs.MFCS.2021.84},
  annote =	{Keywords: Cayley graphs, counting complexity, expander graphs, fine-grained complexity, parameterized complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.91
On Counting (Quantum-)Graph Homomorphisms in Finite Fields of Prime Order

Authors: J. A. Gregor Lagodzinski, Andreas Göbel, Katrin Casel, and Tobias Friedrich

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

Abstract
We study the problem of counting the number of homomorphisms from an input graph G to a fixed (quantum) graph ̄{H} in any finite field of prime order ℤ_p. The subproblem with graph H was introduced by Faben and Jerrum [ToC'15] and its complexity is still uncharacterised despite active research, e.g. the very recent work of Focke, Goldberg, Roth, and Zivný [SODA'21]. Our contribution is threefold. First, we introduce the study of quantum graphs to the study of modular counting homomorphisms. We show that the complexity for a quantum graph ̄{H} collapses to the complexity criteria found at dimension 1: graphs. Second, in order to prove cases of intractability we establish a further reduction to the study of bipartite graphs. Lastly, we establish a dichotomy for all bipartite (K_{3,3}$1{e}, {domino})-free graphs by a thorough structural study incorporating both local and global arguments. This result subsumes all results on bipartite graphs known for all prime moduli and extends them significantly. Even for the subproblem with p = 2 this establishes new results.
Cite as

J. A. Gregor Lagodzinski, Andreas Göbel, Katrin Casel, and Tobias Friedrich. On Counting (Quantum-)Graph Homomorphisms in Finite Fields of Prime Order. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 91:1-91:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lagodzinski_et_al:LIPIcs.ICALP.2021.91,
  author =	{Lagodzinski, J. A. Gregor and G\"{o}bel, Andreas and Casel, Katrin and Friedrich, Tobias},
  title =	{{On Counting (Quantum-)Graph Homomorphisms in Finite Fields of Prime Order}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{91:1--91:15},
  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.2021.91},
  URN =		{urn:nbn:de:0030-drops-141608},
  doi =		{10.4230/LIPIcs.ICALP.2021.91},
  annote =	{Keywords: Algorithms, Theory, Quantum Graphs, Bipartite Graphs, Graph Homomorphisms, Modular Counting, Complexity Dichotomy}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.5
Chasing Puppies: Mobile Beacon Routing on Closed Curves

Authors: Mikkel Abrahamsen, Jeff Erickson, Irina Kostitsyna, Maarten Löffler, Tillmann Miltzow, Jérôme Urhausen, Jordi Vermeulen, and Giovanni Viglietta

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
We solve an open problem posed by Michael Biro at CCCG 2013 that was inspired by his and others’ work on beacon-based routing. Consider a human and a puppy on a simple closed curve in the plane. The human can walk along the curve at bounded speed and change direction as desired. The puppy runs with unbounded speed along the curve as long as the Euclidean straight-line distance to the human is decreasing, so that it is always at a point on the curve where the distance is locally minimal. Assuming that the curve is smooth (with some mild genericity constraints) or a simple polygon, we prove that the human can always catch the puppy in finite time.
Cite as

Mikkel Abrahamsen, Jeff Erickson, Irina Kostitsyna, Maarten Löffler, Tillmann Miltzow, Jérôme Urhausen, Jordi Vermeulen, and Giovanni Viglietta. Chasing Puppies: Mobile Beacon Routing on Closed Curves. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2021.5,
  author =	{Abrahamsen, Mikkel and Erickson, Jeff and Kostitsyna, Irina and L\"{o}ffler, Maarten and Miltzow, Tillmann and Urhausen, J\'{e}r\^{o}me and Vermeulen, Jordi and Viglietta, Giovanni},
  title =	{{Chasing Puppies: Mobile Beacon Routing on Closed Curves}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.5},
  URN =		{urn:nbn:de:0030-drops-138046},
  doi =		{10.4230/LIPIcs.SoCG.2021.5},
  annote =	{Keywords: Beacon routing, navigation, generic smooth curves, puppies}
}
Document
DOI: 10.4230/DagMan.9.1.43
Diversity in News Recommendation (Dagstuhl Perspectives Workshop 19482)

Authors: Abraham Bernstein, Claes de Vreese, Natali Helberger, Wolfgang Schulz, Katharina Zweig, Christian Baden, Michael A. Beam, Marc P. Hauer, Lucien Heitz, Pascal Jürgens, Christian Katzenbach, Benjamin Kille, Beate Klimkiewicz, Wiebke Loosen, Judith Moeller, Goran Radanovic, Guy Shani, Nava Tintarev, Suzanne Tolmeijer, Wouter van Atteveldt, Sanne Vrijenhoek, and Theresa Zueger

Published in: Dagstuhl Manifestos, Volume 9, Issue 1 (2021)

Abstract
News diversity in the media has for a long time been a foundational and uncontested basis for ensuring that the communicative needs of individuals and society at large are met. Today, people increasingly rely on online content and recommender systems to consume information challenging the traditional concept of news diversity. In addition, the very concept of diversity, which differs between disciplines, will need to be re-evaluated requiring an interdisciplinary investigation, which requires a new level of mutual cooperation between computer scientists, social scientists, and legal scholars. Based on the outcome of a interdisciplinary workshop, we have the following recommendations, directed at researchers, funders, legislators, regulators, and the media industry: - Conduct interdisciplinary research on news recommenders and diversity. - Create a safe harbor for academic research with industry data. - Strengthen the role of public values in news recommenders. - Create a meaningful governance framework for news recommenders. - Fund a joint lab to spearhead the needed interdisciplinary research, boost practical innovation, develop reference solutions, and transfer insights into practice.
Cite as

Abraham Bernstein, Claes de Vreese, Natali Helberger, Wolfgang Schulz, Katharina Zweig, Christian Baden, Michael A. Beam, Marc P. Hauer, Lucien Heitz, Pascal Jürgens, Christian Katzenbach, Benjamin Kille, Beate Klimkiewicz, Wiebke Loosen, Judith Moeller, Goran Radanovic, Guy Shani, Nava Tintarev, Suzanne Tolmeijer, Wouter van Atteveldt, Sanne Vrijenhoek, and Theresa Zueger. Diversity in News Recommendation (Dagstuhl Perspectives Workshop 19482). In Dagstuhl Manifestos, Volume 9, Issue 1, pp. 43-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Article{bernstein_et_al:DagMan.9.1.43,
  author =	{Bernstein, Abraham and de Vreese, Claes and Helberger, Natali and Schulz, Wolfgang and Zweig, Katharina and Baden, Christian and Beam, Michael A. and Hauer, Marc P. and Heitz, Lucien and J\"{u}rgens, Pascal and Katzenbach, Christian and Kille, Benjamin and Klimkiewicz, Beate and Loosen, Wiebke and Moeller, Judith and Radanovic, Goran and Shani, Guy and Tintarev, Nava and Tolmeijer, Suzanne and van Atteveldt, Wouter and Vrijenhoek, Sanne and Zueger, Theresa},
  title =	{{Diversity in News Recommendation (Dagstuhl Perspectives Workshop 19482)}},
  pages =	{43--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2021},
  volume =	{9},
  number =	{1},
  editor =	{Bernstein, Abraham and de Vreese, Claes and Helberger, Natali and Schulz, Wolfgang and Zweig, Katharina and Baden, Christian and Beam, Michael A. and Hauer, Marc P. and Heitz, Lucien and J\"{u}rgens, Pascal and Katzenbach, Christian and Kille, Benjamin and Klimkiewicz, Beate and Loosen, Wiebke and Moeller, Judith and Radanovic, Goran and Shani, Guy and Tintarev, Nava and Tolmeijer, Suzanne and van Atteveldt, Wouter and Vrijenhoek, Sanne and Zueger, Theresa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagMan.9.1.43},
  URN =		{urn:nbn:de:0030-drops-137456},
  doi =		{10.4230/DagMan.9.1.43},
  annote =	{Keywords: News, recommender systems, diversity}
}
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