Published in: OASIcs, Volume 139, 1st New Ideas in Networked Systems (NINeS 2026)
Guillermo Baltra, Tarang Saluja, Yuri Pradkin, and John Heidemann. Understanding Partial Reachability in the Internet Core. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 4:1-4:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
@InProceedings{baltra_et_al:OASIcs.NINeS.2026.4,
author = {Baltra, Guillermo and Saluja, Tarang and Pradkin, Yuri and Heidemann, John},
title = {{Understanding Partial Reachability in the Internet Core}},
booktitle = {1st New Ideas in Networked Systems (NINeS 2026)},
pages = {4:1--4:32},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-414-7},
ISSN = {2190-6807},
year = {2026},
volume = {139},
editor = {Argyraki, Katerina and Panda, Aurojit},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NINeS.2026.4},
URN = {urn:nbn:de:0030-drops-255892},
doi = {10.4230/OASIcs.NINeS.2026.4},
annote = {Keywords: Internet, Internet reliability, Network outages, Active measurements}
}
Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)
Timothé Albouy, Davide Frey, Mathieu Gestin, Michel Raynal, and François Taïani. Contention-Aware Cooperation. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@InProceedings{albouy_et_al:LIPIcs.OPODIS.2025.9,
author = {Albouy, Timoth\'{e} and Frey, Davide and Gestin, Mathieu and Raynal, Michel and Ta\"{i}ani, Fran\c{c}ois},
title = {{Contention-Aware Cooperation}},
booktitle = {29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
pages = {9:1--9:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-409-3},
ISSN = {1868-8969},
year = {2026},
volume = {361},
editor = {Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.9},
URN = {urn:nbn:de:0030-drops-251823},
doi = {10.4230/LIPIcs.OPODIS.2025.9},
annote = {Keywords: Agreement, Asynchronous message-passing system, Byzantine processes, Conflict detection, Consensus, Cooperation abstraction, Distributed computing, Fault tolerance, Optimistically terminating consensus, Short-naming}
}
Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)
Umang Bhaskar and Yeshwant Pandit. Extending EFX Allocations to Further Multi-Graph Classes. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@InProceedings{bhaskar_et_al:LIPIcs.FSTTCS.2025.15,
author = {Bhaskar, Umang and Pandit, Yeshwant},
title = {{Extending EFX Allocations to Further Multi-Graph Classes}},
booktitle = {45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
pages = {15:1--15:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-406-2},
ISSN = {1868-8969},
year = {2025},
volume = {360},
editor = {Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.15},
URN = {urn:nbn:de:0030-drops-250958},
doi = {10.4230/LIPIcs.FSTTCS.2025.15},
annote = {Keywords: Fair Division, EFX, Multi-graphs}
}
Published in: TGDK, Volume 3, Issue 2 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 2
Arnab Sharma, N'Dah Jean Kouagou, and Axel-Cyrille Ngonga Ngomo. Resilience in Knowledge Graph Embeddings. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 2, pp. 1:1-1:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@Article{sharma_et_al:TGDK.3.2.1,
author = {Sharma, Arnab and Kouagou, N'Dah Jean and Ngomo, Axel-Cyrille Ngonga},
title = {{Resilience in Knowledge Graph Embeddings}},
journal = {Transactions on Graph Data and Knowledge},
pages = {1:1--1:38},
ISSN = {2942-7517},
year = {2025},
volume = {3},
number = {2},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.2.1},
URN = {urn:nbn:de:0030-drops-248117},
doi = {10.4230/TGDK.3.2.1},
annote = {Keywords: Knowledge graphs, Resilience, Robustness}
}
Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)
Aditya Acharya, Auguste H. Gezalyan, Julian Vanecek, David M. Mount, and Sunil Arya. Support Vector Machines in the Hilbert Geometry. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@InProceedings{acharya_et_al:LIPIcs.WADS.2025.3,
author = {Acharya, Aditya and Gezalyan, Auguste H. and Vanecek, Julian and Mount, David M. and Arya, Sunil},
title = {{Support Vector Machines in the Hilbert Geometry}},
booktitle = {19th International Symposium on Algorithms and Data Structures (WADS 2025)},
pages = {3:1--3:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-398-0},
ISSN = {1868-8969},
year = {2025},
volume = {349},
editor = {Morin, Pat and Oh, Eunjin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.3},
URN = {urn:nbn:de:0030-drops-242348},
doi = {10.4230/LIPIcs.WADS.2025.3},
annote = {Keywords: Support vector machines, Hilbert geometry, linear classification, machine learning, LP-type problems}
}
Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)
Gal Gilad, Teresa M. Przytycka, and Roded Sharan. Mutational Signature Refitting on Sparse Pan-Cancer Data. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@InProceedings{gilad_et_al:LIPIcs.WABI.2025.11,
author = {Gilad, Gal and Przytycka, Teresa M. and Sharan, Roded},
title = {{Mutational Signature Refitting on Sparse Pan-Cancer Data}},
booktitle = {25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
pages = {11:1--11:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-386-7},
ISSN = {1868-8969},
year = {2025},
volume = {344},
editor = {Brejov\'{a}, Bro\v{n}a and Patro, Rob},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.11},
URN = {urn:nbn:de:0030-drops-239374},
doi = {10.4230/LIPIcs.WABI.2025.11},
annote = {Keywords: mutational signatures, signature refitting, cancer genomics, genomic data analysis, somatic mutations}
}
Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)
Nathaniel K. Brown, Travis Gagie, Giovanni Manzini, Gonzalo Navarro, and Marinella Sciortino. Faster Run-Length Compressed Suffix Arrays. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@InProceedings{brown_et_al:OASIcs.Grossi.10,
author = {Brown, Nathaniel K. and Gagie, Travis and Manzini, Giovanni and Navarro, Gonzalo and Sciortino, Marinella},
title = {{Faster Run-Length Compressed Suffix Arrays}},
booktitle = {From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
pages = {10:1--10:15},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-391-1},
ISSN = {2190-6807},
year = {2025},
volume = {132},
editor = {Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.10},
URN = {urn:nbn:de:0030-drops-238095},
doi = {10.4230/OASIcs.Grossi.10},
annote = {Keywords: Run-length compressed suffix arrays, interpolative coding, two-level indexing}
}
Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)
Ragnar Groot Koerkamp and Igor Martayan. SimdMinimizers: Computing Random Minimizers, fast. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@InProceedings{grootkoerkamp_et_al:LIPIcs.SEA.2025.20,
author = {Groot Koerkamp, Ragnar and Martayan, Igor},
title = {{SimdMinimizers: Computing Random Minimizers, fast}},
booktitle = {23rd International Symposium on Experimental Algorithms (SEA 2025)},
pages = {20:1--20:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-375-1},
ISSN = {1868-8969},
year = {2025},
volume = {338},
editor = {Mutzel, Petra and Prezza, Nicola},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.20},
URN = {urn:nbn:de:0030-drops-232581},
doi = {10.4230/LIPIcs.SEA.2025.20},
annote = {Keywords: Minimizers, Randomized algorithms, Sketching, Hashing}
}
Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)
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)
@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}
}
Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)
Carl Friedrich Bolz-Tereick, Luke Panayi, Ferdia McKeogh, Tom Spink, and Martin Berger. Pydrofoil: Accelerating Sail-Based Instruction Set Simulators. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 3:1-3:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@InProceedings{bolztereick_et_al:LIPIcs.ECOOP.2025.3,
author = {Bolz-Tereick, Carl Friedrich and Panayi, Luke and McKeogh, Ferdia and Spink, Tom and Berger, Martin},
title = {{Pydrofoil: Accelerating Sail-Based Instruction Set Simulators}},
booktitle = {39th European Conference on Object-Oriented Programming (ECOOP 2025)},
pages = {3:1--3:31},
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.2025.3},
URN = {urn:nbn:de:0030-drops-232962},
doi = {10.4230/LIPIcs.ECOOP.2025.3},
annote = {Keywords: Instruction set architecture, processor, domain-specific language, just-in-time compilation, meta-tracing}
}
Published in: OASIcs, Volume 128, Sixth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2025)
Diogo Costa, Gonçalo Moreira, Afonso Oliveira, José Martins, and Sandro Pinto. SP-IMPact: A Framework for Static Partitioning Interference Mitigation and Performance Analysis. In Sixth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2025). Open Access Series in Informatics (OASIcs), Volume 128, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@InProceedings{costa_et_al:OASIcs.NG-RES.2025.5,
author = {Costa, Diogo and Moreira, Gon\c{c}alo and Oliveira, Afonso and Martins, Jos\'{e} and Pinto, Sandro},
title = {{SP-IMPact: A Framework for Static Partitioning Interference Mitigation and Performance Analysis}},
booktitle = {Sixth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2025)},
pages = {5:1--5:15},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {978-3-95977-366-9},
ISSN = {2190-6807},
year = {2025},
volume = {128},
editor = {Yomsi, Patrick Meumeu and Wildermann, Stefan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NG-RES.2025.5},
URN = {urn:nbn:de:0030-drops-229911},
doi = {10.4230/OASIcs.NG-RES.2025.5},
annote = {Keywords: Virtualization, Contention, Multi-core Interference, Mixed-Criticality Systems, Arm}
}
Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)
Manuel Lafond, Alitzel López Sánchez, and Weidong Luo. Cluster Editing on Cographs and Related Classes. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 64:1-64:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
@InProceedings{lafond_et_al:LIPIcs.STACS.2025.64,
author = {Lafond, Manuel and L\'{o}pez S\'{a}nchez, Alitzel and Luo, Weidong},
title = {{Cluster Editing on Cographs and Related Classes}},
booktitle = {42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
pages = {64:1--64:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-365-2},
ISSN = {1868-8969},
year = {2025},
volume = {327},
editor = {Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.64},
URN = {urn:nbn:de:0030-drops-228895},
doi = {10.4230/LIPIcs.STACS.2025.64},
annote = {Keywords: Cluster editing, cographs, parameterized algorithms, clique-width, trivially perfect graphs}
}
Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)
Mario M. Alvarez, Henry Arneson, Ben Berger, Lee Bousfield, Chris Buckland, Yafah Edelman, Edward W. Felten, Daniel Goldman, Raul Jordan, Mahimna Kelkar, Akaki Mamageishvili, Harry Ng, Aman Sanghi, Victor Shoup, and Terence Tsao. BoLD: Fast and Cheap Dispute Resolution. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{alvarez_et_al:LIPIcs.AFT.2024.2,
author = {Alvarez, Mario M. and Arneson, Henry and Berger, Ben and Bousfield, Lee and Buckland, Chris and Edelman, Yafah and Felten, Edward W. and Goldman, Daniel and Jordan, Raul and Kelkar, Mahimna and Mamageishvili, Akaki and Ng, Harry and Sanghi, Aman and Shoup, Victor and Tsao, Terence},
title = {{BoLD: Fast and Cheap Dispute Resolution}},
booktitle = {6th Conference on Advances in Financial Technologies (AFT 2024)},
pages = {2:1--2:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-345-4},
ISSN = {1868-8969},
year = {2024},
volume = {316},
editor = {B\"{o}hme, Rainer and Kiffer, Lucianna},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.2},
URN = {urn:nbn:de:0030-drops-209389},
doi = {10.4230/LIPIcs.AFT.2024.2},
annote = {Keywords: Optimistic rollups, fraud proofs}
}
Published in: LITES, Volume 6, Issue 1 (2019). Leibniz Transactions on Embedded Systems, Volume 6, Issue 1
Robert I. Davis and Liliana Cucu-Grosjean. A Survey of Probabilistic Schedulability Analysis Techniques for Real-Time Systems. In LITES, Volume 6, Issue 1 (2019). Leibniz Transactions on Embedded Systems, Volume 6, Issue 1, pp. 04:1-04:53, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@Article{davis_et_al:LITES-v006-i001-a004,
author = {Davis, Robert I. and Cucu-Grosjean, Liliana},
title = {{A Survey of Probabilistic Schedulability Analysis Techniques for Real-Time Systems}},
journal = {Leibniz Transactions on Embedded Systems},
pages = {04:1--04:53},
ISSN = {2199-2002},
year = {2019},
volume = {6},
number = {1},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LITES-v006-i001-a004},
URN = {urn:nbn:de:0030-drops-192803},
doi = {10.4230/LITES-v006-i001-a004},
annote = {Keywords: Probabilistic, real-time, schedulability analysis, scheduling, }
}
Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Ben Berger and Zvika Brakerski. Brief Announcement: Zero-Knowledge Protocols for Search Problems. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 105:1-105:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
@InProceedings{berger_et_al:LIPIcs.ICALP.2018.105,
author = {Berger, Ben and Brakerski, Zvika},
title = {{Brief Announcement: Zero-Knowledge Protocols for Search Problems}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {105:1--105:5},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-076-7},
ISSN = {1868-8969},
year = {2018},
volume = {107},
editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.105},
URN = {urn:nbn:de:0030-drops-91099},
doi = {10.4230/LIPIcs.ICALP.2018.105},
annote = {Keywords: Zero-Knowledge, Search Problems, Interactive Proofs}
}