8 Search Results for "Püschel, Markus"

Document
DOI: 10.4230/LIPIcs.FUN.2026.11
An Almost-Optimal Upper Bound on the Push Number of the Torus Puzzle

Authors: Matteo Caporrella and Stefano Leucci

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
We study the Torus Puzzle, a solitaire game in which the elements of an input m × n matrix need to be rearranged into a target configuration via a sequence of unit rotations (i.e., circular shifts) of rows and/or columns. Amano et al. proposed a more permissive variant of the above puzzle, where each row and column rotation can shift the involved elements by any amount of positions. The number of rotations needed to solve the original and the permissive variants of the puzzle are respectively known as the push number and the drag number, where the latter is always smaller than or equal to the former and admits an existential lower bound of Ω(mn). While this lower bound is matched by an O(mn) upper bound, the push number is not so well understood. Indeed, to the best of our knowledge, only an O(mn ⋅ max{m, n}) upper bound is currently known. In this paper, we provide an algorithm that solves the Torus Puzzle using O(mn ⋅ log max {m, n}) unit rotations in a model that is more restricted than that of the original puzzle. This implies a corresponding upper bound on the push number and reduces the gap between the known upper and lower bounds from Θ(max{m,n}) to Θ(log max{m, n}).
Cite as

Matteo Caporrella and Stefano Leucci. An Almost-Optimal Upper Bound on the Push Number of the Torus Puzzle. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{caporrella_et_al:LIPIcs.FUN.2026.11,
  author =	{Caporrella, Matteo and Leucci, Stefano},
  title =	{{An Almost-Optimal Upper Bound on the Push Number of the Torus Puzzle}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.11},
  URN =		{urn:nbn:de:0030-drops-257307},
  doi =		{10.4230/LIPIcs.FUN.2026.11},
  annote =	{Keywords: Torus puzzle, Push number, Permutation puzzles}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2025.2
Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk)

Authors: Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Neuro-symbolic programs, i.e. programs containing both machine learning components and traditional symbolic code, are becoming increasingly widespread. Finding a general methodology for verifying such programs is challenging due to both the number of different tools involved and the intricate interface between the "neural" and "symbolic" program components. In this paper we present a general decomposition of the neuro-symbolic verification problem into parts, and examine the problem of the embedding gap that occurs when one tries to combine proofs about the neural and symbolic components. To address this problem we then introduce Vehicle - standing as an abbreviation for a "verification condition language" - an intermediate programming language interface between machine learning frameworks, automated theorem provers, and dependently-typed formalisations of neuro-symbolic programs. Vehicle allows users to specify the properties of the neural components of neuro-symbolic programs once, and then safely compile the specification to each interface using a tailored typing and compilation procedure. We give a high-level overview of Vehicle’s overall design, its interfaces and compilation & type-checking procedures, and then demonstrate its utility by formally verifying the safety of a simple autonomous car controlled by a neural network, operating in a stochastic environment with imperfect information.
Cite as

Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi. Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk). In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 2:1-2:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{daggitt_et_al:LIPIcs.FSCD.2025.2,
  author =	{Daggitt, Matthew L. and Kokke, Wen and Atkey, Robert and Komendantskaya, Ekaterina and Slusarz, Natalia and Arnaboldi, Luca},
  title =	{{Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{2:1--2:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.2},
  URN =		{urn:nbn:de:0030-drops-236172},
  doi =		{10.4230/LIPIcs.FSCD.2025.2},
  annote =	{Keywords: Neural Network Verification, Types, Interactive Theorem Provers}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.36
Efficient Neural Network Verification via Order Leading Exploration of Branch-and-Bound Trees

Authors: Guanqin Zhang, Kota Fukuda, Zhenya Zhang, H.M.N. Dilum Bandara, Shiping Chen, Jianjun Zhao, and Yulei Sui

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract
The vulnerability of neural networks to adversarial perturbations has necessitated formal verification techniques that can rigorously certify the quality of neural networks. As the state-of-the-art, branch-and-bound (BaB) is a "divide-and-conquer" strategy that applies off-the-shelf verifiers to sub-problems for which they perform better. While BaB can identify the sub-problems that are necessary to be split, it explores the space of these sub-problems in a naive "first-come-first-served" manner, thereby suffering from an issue of inefficiency to reach a verification conclusion. To bridge this gap, we introduce an order over different sub-problems produced by BaB, concerning with their different likelihoods of containing counterexamples. Based on this order, we propose a novel verification framework Oliva that explores the sub-problem space by prioritizing those sub-problems that are more likely to find counterexamples, in order to efficiently reach the conclusion of the verification. Even if no counterexample can be found in any sub-problem, it only changes the order of visiting different sub-problems and so will not lead to a performance degradation. Specifically, Oliva has two variants, including Oliva^GR, a greedy strategy that always prioritizes the sub-problems that are more likely to find counterexamples, and Oliva^SA, a balanced strategy inspired by simulated annealing that gradually shifts from exploration to exploitation to locate the globally optimal sub-problems. We experimentally evaluate the performance of Oliva on 690 verification problems spanning over 5 models with datasets MNIST and CIFAR-10. Compared to the state-of-the-art approaches, we demonstrate the speedup of Oliva for up to 25× in MNIST, and up to 80× in CIFAR-10.
Cite as

Guanqin Zhang, Kota Fukuda, Zhenya Zhang, H.M.N. Dilum Bandara, Shiping Chen, Jianjun Zhao, and Yulei Sui. Efficient Neural Network Verification via Order Leading Exploration of Branch-and-Bound Trees. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 36:1-36:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang_et_al:LIPIcs.ECOOP.2025.36,
  author =	{Zhang, Guanqin and Fukuda, Kota and Zhang, Zhenya and Bandara, H.M.N. Dilum and Chen, Shiping and Zhao, Jianjun and Sui, Yulei},
  title =	{{Efficient Neural Network Verification via Order Leading Exploration of Branch-and-Bound Trees}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{36:1--36:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan 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.ECOOP.2025.36},
  URN =		{urn:nbn:de:0030-drops-233281},
  doi =		{10.4230/LIPIcs.ECOOP.2025.36},
  annote =	{Keywords: neural network verification, branch and bound, counterexample potentiality, simulated annealing, stochastic optimization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.33
Faster Sparse Matrix Inversion and Rank Computation in Finite Fields

Authors: Sílvia Casacuberta and Rasmus Kyng

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected O(n^{2.2131}) time for the current values of fast rectangular matrix multiplication. We achieve the same running time for the computation of the rank and nullspace of a sparse matrix over a finite field. This improvement relies on two key techniques. First, we adopt the decomposition of an arbitrary matrix into block Krylov and Hankel matrices from Eberly et al. (ISSAC 2007). Second, we show how to recover the explicit inverse of a block Hankel matrix using low displacement rank techniques for structured matrices and fast rectangular matrix multiplication algorithms. We generalize our inversion method to block structured matrices with other displacement operators and strengthen the best known upper bounds for explicit inversion of block Toeplitz-like and block Hankel-like matrices, as well as for explicit inversion of block Vandermonde-like matrices with structured blocks. As a further application, we improve the complexity of several algorithms in topological data analysis and in finite group theory.
Cite as

Sílvia Casacuberta and Rasmus Kyng. Faster Sparse Matrix Inversion and Rank Computation in Finite Fields. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{casacuberta_et_al:LIPIcs.ITCS.2022.33,
  author =	{Casacuberta, S{\'\i}lvia and Kyng, Rasmus},
  title =	{{Faster Sparse Matrix Inversion and Rank Computation in Finite Fields}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{33:1--33:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.33},
  URN =		{urn:nbn:de:0030-drops-156290},
  doi =		{10.4230/LIPIcs.ITCS.2022.33},
  annote =	{Keywords: Matrix inversion, rank computation, displacement operators, numerical linear algebra}
}
Document
DOI: 10.4230/LIPIcs.SNAPL.2015.238
Go Meta! A Case for Generative Programming and DSLs in Performance Critical Systems

Authors: Tiark Rompf, Kevin J. Brown, HyoukJoong Lee, Arvind K. Sujeeth, Manohar Jonnalagedda, Nada Amin, Georg Ofenbeck, Alen Stojanov, Yannis Klonatos, Mohammad Dashti, Christoph Koch, Markus Püschel, and Kunle Olukotun

Published in: LIPIcs, Volume 32, 1st Summit on Advances in Programming Languages (SNAPL 2015)

Abstract
Most performance critical software is developed using very low-level techniques. We argue that this needs to change, and that generative programming is an effective avenue to enable the use of high-level languages and programming techniques in many such circumstances.
Cite as

Tiark Rompf, Kevin J. Brown, HyoukJoong Lee, Arvind K. Sujeeth, Manohar Jonnalagedda, Nada Amin, Georg Ofenbeck, Alen Stojanov, Yannis Klonatos, Mohammad Dashti, Christoph Koch, Markus Püschel, and Kunle Olukotun. Go Meta! A Case for Generative Programming and DSLs in Performance Critical Systems. In 1st Summit on Advances in Programming Languages (SNAPL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 32, pp. 238-261, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{rompf_et_al:LIPIcs.SNAPL.2015.238,
  author =	{Rompf, Tiark and Brown, Kevin J. and Lee, HyoukJoong and Sujeeth, Arvind K. and Jonnalagedda, Manohar and Amin, Nada and Ofenbeck, Georg and Stojanov, Alen and Klonatos, Yannis and Dashti, Mohammad and Koch, Christoph and P\"{u}schel, Markus and Olukotun, Kunle},
  title =	{{Go Meta! A Case for Generative Programming and DSLs in Performance Critical Systems}},
  booktitle =	{1st Summit on Advances in Programming Languages (SNAPL 2015)},
  pages =	{238--261},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-80-4},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{32},
  editor =	{Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2015.238},
  URN =		{urn:nbn:de:0030-drops-50295},
  doi =		{10.4230/LIPIcs.SNAPL.2015.238},
  annote =	{Keywords: Performance, Generative Programming, Staging, DSLs}
}
Document
DOI: 10.4230/DagSemProc.10191.1
10191 Abstracts Collection – Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond

Authors: Christoph W. Kessler, Welf Löwe, David Padua, and Markus Püschel

Published in: Dagstuhl Seminar Proceedings, Volume 10191, Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond (2010)

Abstract
From May 9 to 12, 2010, the Dagstuhl Seminar 10191 ``Program Composition and Optimization: Autotuning, Scheduling, Metaprogramming and Beyond'' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Christoph W. Kessler, Welf Löwe, David Padua, and Markus Püschel. 10191 Abstracts Collection – Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond. In Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond. Dagstuhl Seminar Proceedings, Volume 10191, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{kessler_et_al:DagSemProc.10191.1,
  author =	{Kessler, Christoph W. and L\"{o}we, Welf and Padua, David and P\"{u}schel, Markus},
  title =	{{10191 Abstracts Collection – Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond}},
  booktitle =	{Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10191},
  editor =	{Christoph W. Kessler and Welf L\"{o}we and David Padua and Markus P\"{u}schel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10191.1},
  URN =		{urn:nbn:de:0030-drops-25726},
  doi =		{10.4230/DagSemProc.10191.1},
  annote =	{Keywords: Software composition, program optimization, components, parallel computing, scheduling, autotuning, adaptivity, performance prediction, library synthesis, meta-programming}
}
Document
DOI: 10.4230/DagSemProc.10191.2
10191 Executive Summary – Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond

Authors: Christoph W. Kessler, Welf Löwe, David Padua, and Markus Püschel

Published in: Dagstuhl Seminar Proceedings, Volume 10191, Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond (2010)

Abstract
Components are a well-proven means of handling software complexity. Reusable components and software composition support the construction of large and reliable software systems from pre-defined and tested partial solutions. When maximizing reusability, we end up with components that are very general and do not fit one particular scenario perfectly. Therefore, adaptation, especially optimization, is established as a technique to deal with such mismatches.
Cite as

Christoph W. Kessler, Welf Löwe, David Padua, and Markus Püschel. 10191 Executive Summary – Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond. In Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond. Dagstuhl Seminar Proceedings, Volume 10191, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{kessler_et_al:DagSemProc.10191.2,
  author =	{Kessler, Christoph W. and L\"{o}we, Welf and Padua, David and P\"{u}schel, Markus},
  title =	{{10191 Executive Summary – Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond}},
  booktitle =	{Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10191},
  editor =	{Christoph W. Kessler and Welf L\"{o}we and David Padua and Markus P\"{u}schel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10191.2},
  URN =		{urn:nbn:de:0030-drops-25712},
  doi =		{10.4230/DagSemProc.10191.2},
  annote =	{Keywords: Software composition, program optimization, components, parallel computing, scheduling, autotuning, adaptivity, performance prediction, library synthesis, meta-programming}
}
Document
DOI: 10.4230/DagSemProc.10191.3
Program Composition and Optimization: An Introduction

Authors: Christoph W. Kessler, Welf Löwe, David Padua, and Markus Püschel

Published in: Dagstuhl Seminar Proceedings, Volume 10191, Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond (2010)

Abstract
Software composition connects separately defined software artifacts. Such connection may be in program structure (such as inheritance), data flow (such as message passing) and/or control flow (such as function calls or loop control).
Cite as

Christoph W. Kessler, Welf Löwe, David Padua, and Markus Püschel. Program Composition and Optimization: An Introduction. In Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond. Dagstuhl Seminar Proceedings, Volume 10191, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{kessler_et_al:DagSemProc.10191.3,
  author =	{Kessler, Christoph W. and L\"{o}we, Welf and Padua, David and P\"{u}schel, Markus},
  title =	{{Program Composition and Optimization: An Introduction}},
  booktitle =	{Program Composition and Optimization : Autotuning, Scheduling, Metaprogramming and Beyond},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10191},
  editor =	{Christoph W. Kessler and Welf L\"{o}we and David Padua and Markus P\"{u}schel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10191.3},
  URN =		{urn:nbn:de:0030-drops-25738},
  doi =		{10.4230/DagSemProc.10191.3},
  annote =	{Keywords: Software composition, program optimization, components, parallel computing, scheduling, autotuning, adaptivity, performance prediction, library synthesis, meta-programming}
}
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