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Documents authored by Schürmann, Carsten

Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2024.39
Robust Mean Estimation by All Means (Short Paper)

Authors: Reynald Affeldt, Clark Barrett, Alessandro Bruni, Ieva Daukantas, Harun Khan, Takafumi Saikawa, and Carsten Schürmann

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
We report the results of a verification experiment on an algorithm for robust mean estimation, i.e., an algorithm that computes a mean in the presence of outliers. We formalize the algorithm in the Coq proof assistant and devise a pragmatic approach for identifying and solving issues related to the choice of bounds. To keep our formalization succinct and generic, we recast the original argument using an existing library for finite probabilities that we extend with reusable lemmas. To formalize the original algorithm, which relies on a subtle convergence argument, we observe that by adding suitable termination checks, we can turn it into a well-founded recursion without losing its original properties. We also exploit a tactic for solving real-valued inequalities by approximation to heuristically fix inaccurate constant values in the original proof.
Cite as

Reynald Affeldt, Clark Barrett, Alessandro Bruni, Ieva Daukantas, Harun Khan, Takafumi Saikawa, and Carsten Schürmann. Robust Mean Estimation by All Means (Short Paper). In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 39:1-39:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{affeldt_et_al:LIPIcs.ITP.2024.39,
  author =	{Affeldt, Reynald and Barrett, Clark and Bruni, Alessandro and Daukantas, Ieva and Khan, Harun and Saikawa, Takafumi and Sch\"{u}rmann, Carsten},
  title =	{{Robust Mean Estimation by All Means}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{39:1--39:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.39},
  URN =		{urn:nbn:de:0030-drops-207679},
  doi =		{10.4230/LIPIcs.ITP.2024.39},
  annote =	{Keywords: robust statistics, probability theory, formal verification}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2016.33
Coherence Generalises Duality: A Logical Explanation of Multiparty Session Types

Authors: Marco Carbone, Sam Lindley, Fabrizio Montesi, Carsten Schürmann, and Philip Wadler

Published in: LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

Abstract
Wadler introduced Classical Processes (CP), a calculus based on a propositions-as-types correspondence between propositions of classical linear logic and session types. Carbone et al. introduced Multiparty Classical Processes, a calculus that generalises CP to multiparty session types, by replacing the duality of classical linear logic (relating two types) with a more general notion of coherence (relating an arbitrary number of types). This paper introduces variants of CP and MCP, plus a new intermediate calculus of Globally-governed Classical Processes (GCP). We show a tight relation between these three calculi, giving semantics-preserving translations from GCP to CP and from MCP to GCP. The translation from GCP to CP interprets a coherence proof as an arbiter process that mediates communications in a session, while MCP adds annotations that permit processes to communicate directly without centralised control.
Cite as

Marco Carbone, Sam Lindley, Fabrizio Montesi, Carsten Schürmann, and Philip Wadler. Coherence Generalises Duality: A Logical Explanation of Multiparty Session Types. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{carbone_et_al:LIPIcs.CONCUR.2016.33,
  author =	{Carbone, Marco and Lindley, Sam and Montesi, Fabrizio and Sch\"{u}rmann, Carsten and Wadler, Philip},
  title =	{{Coherence Generalises Duality: A Logical Explanation of Multiparty Session Types}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{33:1--33:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-017-0},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{59},
  editor =	{Desharnais, Jos\'{e}e and Jagadeesan, Radha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.33},
  URN =		{urn:nbn:de:0030-drops-61811},
  doi =		{10.4230/LIPIcs.CONCUR.2016.33},
  annote =	{Keywords: Multiparty Session Types, Linear Logic, Propositions as Types}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2015.412
Multiparty Session Types as Coherence Proofs

Authors: Marco Carbone, Fabrizio Montesi, Carsten Schürmann, and Nobuko Yoshida

Published in: LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015)

Abstract
We propose a Curry-Howard correspondence between a language for programming multiparty sessions and a generalisation of Classical Linear Logic (CLL). In this framework, propositions correspond to the local behaviour of a participant in a multiparty session type, proofs to processes, and proof normalisation to executing communications. Our key contribution is generalising duality, from CLL, to a new notion of n-ary compatibility, called coherence. Building on coherence as a principle of compositionality, we generalise the cut rule of CLL to a new rule for composing many processes communicating in a multiparty session. We prove the soundness of our model by showing the admissibility of our new rule, which entails deadlock-freedom via our correspondence.
Cite as

Marco Carbone, Fabrizio Montesi, Carsten Schürmann, and Nobuko Yoshida. Multiparty Session Types as Coherence Proofs. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 412-426, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{carbone_et_al:LIPIcs.CONCUR.2015.412,
  author =	{Carbone, Marco and Montesi, Fabrizio and Sch\"{u}rmann, Carsten and Yoshida, Nobuko},
  title =	{{Multiparty Session Types as Coherence Proofs}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{412--426},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Aceto, Luca and de Frutos Escrig, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.412},
  URN =		{urn:nbn:de:0030-drops-53661},
  doi =		{10.4230/LIPIcs.CONCUR.2015.412},
  annote =	{Keywords: Programming languages, Type systems, Session Types, Linear Logic}
}
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