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Documents authored by Nipkow, Tobias


Document
Real-Time Double-Ended Queue Verified (Proof Pearl)

Authors: Balazs Toth and Tobias Nipkow

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)


Abstract
We present the first verification of the real-time doubled-ended queue by Chuang and Goldberg where all operations take constant time. The main contributions are the full system invariant, the precise definition of all abstraction functions, the structure of the proof and the main lemmas.

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Balazs Toth and Tobias Nipkow. Real-Time Double-Ended Queue Verified (Proof Pearl). In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 29:1-29:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{toth_et_al:LIPIcs.ITP.2023.29,
  author =	{Toth, Balazs and Nipkow, Tobias},
  title =	{{Real-Time Double-Ended Queue Verified (Proof Pearl)}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.29},
  URN =		{urn:nbn:de:0030-drops-184044},
  doi =		{10.4230/LIPIcs.ITP.2023.29},
  annote =	{Keywords: Double-ended queue, data structures, verification, Isabelle}
}
Document
Proof Pearl: Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra

Authors: Peter Lammich and Tobias Nipkow

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)


Abstract
The starting point of this paper is a new, purely functional, simple and efficient data structure combining a search tree and a priority queue, which we call a priority search tree. The salient feature of priority search trees is that they offer a decrease-key operation, something that is missing from other simple, purely functional priority queue implementations. As two applications of this data structure we verify purely functional, simple and efficient implementations of Prim’s and Dijkstra’s algorithms. This constitutes the first verification of an executable and even efficient version of Prim’s algorithm.

Cite as

Peter Lammich and Tobias Nipkow. Proof Pearl: Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{lammich_et_al:LIPIcs.ITP.2019.23,
  author =	{Lammich, Peter and Nipkow, Tobias},
  title =	{{Proof Pearl: Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.23},
  URN =		{urn:nbn:de:0030-drops-110788},
  doi =		{10.4230/LIPIcs.ITP.2019.23},
  annote =	{Keywords: Priority queue, Dijkstra’s algorithm, Prim’s algorithm, verification, Isabelle}
}
Document
Invited Talk
Trustworthy Graph Algorithms (Invited Talk)

Authors: Mohammad Abdulaziz, Kurt Mehlhorn, and Tobias Nipkow

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
The goal of the LEDA project was to build an easy-to-use and extendable library of correct and efficient data structures, graph algorithms and geometric algorithms. We report on the use of formal program verification to achieve an even higher level of trustworthiness. Specifically, we report on an ongoing and largely finished verification of the blossom-shrinking algorithm for maximum cardinality matching.

Cite as

Mohammad Abdulaziz, Kurt Mehlhorn, and Tobias Nipkow. Trustworthy Graph Algorithms (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{abdulaziz_et_al:LIPIcs.MFCS.2019.1,
  author =	{Abdulaziz, Mohammad and Mehlhorn, Kurt and Nipkow, Tobias},
  title =	{{Trustworthy Graph Algorithms}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.1},
  URN =		{urn:nbn:de:0030-drops-109456},
  doi =		{10.4230/LIPIcs.MFCS.2019.1},
  annote =	{Keywords: graph algorithms, formal correct proofs, Isabelle, LEDA, certifying algorithms}
}
Document
Formalized Proof Systems for Propositional Logic

Authors: Julius Michaelis and Tobias Nipkow

Published in: LIPIcs, Volume 104, 23rd International Conference on Types for Proofs and Programs (TYPES 2017)


Abstract
We have formalized a range of proof systems for classical propositional logic (sequent calculus, natural deduction, Hilbert systems, resolution) in Isabelle/HOL and have proved the most important meta-theoretic results about semantics and proofs: compactness, soundness, completeness, translations between proof systems, cut-elimination, interpolation and model existence.

Cite as

Julius Michaelis and Tobias Nipkow. Formalized Proof Systems for Propositional Logic. In 23rd International Conference on Types for Proofs and Programs (TYPES 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 104, pp. 5:1-5:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{michaelis_et_al:LIPIcs.TYPES.2017.5,
  author =	{Michaelis, Julius and Nipkow, Tobias},
  title =	{{Formalized Proof Systems for Propositional Logic}},
  booktitle =	{23rd International Conference on Types for Proofs and Programs (TYPES 2017)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-071-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{104},
  editor =	{Abel, Andreas and Nordvall Forsberg, Fredrik and Kaposi, Ambrus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2017.5},
  URN =		{urn:nbn:de:0030-drops-100537},
  doi =		{10.4230/LIPIcs.TYPES.2017.5},
  annote =	{Keywords: formalization of logic, proof systems, sequent calculus, natural deduction, resolution}
}
Document
Verified Analysis of List Update Algorithms

Authors: Maximilian P. L. Haslbeck and Tobias Nipkow

Published in: LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)


Abstract
This paper presents a machine-verified analysis of a number of classical algorithms for the list update problem: 2-competitiveness of move-to-front, the lower bound of 2 for the competitiveness of deterministic list update algorithms and 1.6-competitiveness of the randomized COMB algorithm, the best randomized list update algorithm known to date. The analysis is verified with help of the theorem prover Isabelle; some low-level proofs could be automated.

Cite as

Maximilian P. L. Haslbeck and Tobias Nipkow. Verified Analysis of List Update Algorithms. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 49:1-49:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{haslbeck_et_al:LIPIcs.FSTTCS.2016.49,
  author =	{Haslbeck, Maximilian P. L. and Nipkow, Tobias},
  title =	{{Verified Analysis of List Update Algorithms}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{49:1--49:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.49},
  URN =		{urn:nbn:de:0030-drops-68849},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.49},
  annote =	{Keywords: Program Verification, Algorithm Analysis, Online Algorithms}
}
Document
Verified Analysis of Functional Data Structures

Authors: Tobias Nipkow

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)


Abstract
In recent work the author has analyzed a number of classical functional search tree and priority queue implementations with the help of the theorem prover Isabelle/HOL. The functional correctness proofs of AVL trees, red-black trees, 2-3 trees, 2-3-4 trees, 1-2 brother trees, AA trees and splay trees could be automated. The amortized logarithmic complexity of skew heaps, splay trees, splay heaps and pairing heaps had to be proved manually.

Cite as

Tobias Nipkow. Verified Analysis of Functional Data Structures. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 4:1-4:2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{nipkow:LIPIcs.FSCD.2016.4,
  author =	{Nipkow, Tobias},
  title =	{{Verified Analysis of Functional Data Structures}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{4:1--4:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.4},
  URN =		{urn:nbn:de:0030-drops-59701},
  doi =		{10.4230/LIPIcs.FSCD.2016.4},
  annote =	{Keywords: Program Verification, Algorithm Analysis, Functional Programming}
}
Document
Deduction and Arithmetic (Dagstuhl Seminar 13411)

Authors: Nikolaj Bjorner, Reiner Hähnle, Tobias Nipkow, and Christoph Weidenbach

Published in: Dagstuhl Reports, Volume 3, Issue 10 (2014)


Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 13411 "Deduction and Arithmetic". The aim of this seminar was to bring together researchers working in deduction and fields related to arithmetic constraint solving. Current research in deduction can be categorized in three main strands: SMT solvers, automated first-order provers, and interactive provers. Although dealing with arithmetic has been in focus of all three for some years, there is still need of much better support of arithmetic. Reasong about arithmetic will stay at the center of attention in all three main approaches to automated deduction during the coming five to ten years. The seminar was an important event for the subcommunities involved that made it possible to communicate with each other so as to avoid duplicate effort and to exploit synergies. It succeeded also in identifying a number of important trends and open problems.

Cite as

Nikolaj Bjorner, Reiner Hähnle, Tobias Nipkow, and Christoph Weidenbach. Deduction and Arithmetic (Dagstuhl Seminar 13411). In Dagstuhl Reports, Volume 3, Issue 10, pp. 1-24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)


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@Article{bjorner_et_al:DagRep.3.10.1,
  author =	{Bjorner, Nikolaj and H\"{a}hnle, Reiner and Nipkow, Tobias and Weidenbach, Christoph},
  title =	{{Deduction and Arithmetic (Dagstuhl Seminar 13411)}},
  pages =	{1--24},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2014},
  volume =	{3},
  number =	{10},
  editor =	{Bjorner, Nikolaj and H\"{a}hnle, Reiner and Nipkow, Tobias and Weidenbach, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.3.10.1},
  URN =		{urn:nbn:de:0030-drops-44250},
  doi =		{10.4230/DagRep.3.10.1},
  annote =	{Keywords: Automated Deduction; Program Verification; Arithmetic Constraint Solving}
}
Document
09411 Abstracts Collection – Interaction versus Automation: The two Faces of Deduction

Authors: Thomas Ball, Jürgen Giesl, Reiner Hähnle, and Tobias Nipkow

Published in: Dagstuhl Seminar Proceedings, Volume 9411, Interaction versus Automation: The two Faces of Deduction (2010)


Abstract
From 04.10. to 09.10.2009, the Dagstuhl Seminar 09411 ``Interaction versus Automation: The two Faces of Deduction'' 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

Thomas Ball, Jürgen Giesl, Reiner Hähnle, and Tobias Nipkow. 09411 Abstracts Collection – Interaction versus Automation: The two Faces of Deduction. In Interaction versus Automation: The two Faces of Deduction. Dagstuhl Seminar Proceedings, Volume 9411, pp. 1-18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{ball_et_al:DagSemProc.09411.1,
  author =	{Ball, Thomas and Giesl, J\"{u}rgen and H\"{a}hnle, Reiner and Nipkow, Tobias},
  title =	{{09411 Abstracts Collection – Interaction versus Automation: The two Faces of Deduction}},
  booktitle =	{Interaction versus Automation: The two Faces of Deduction},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9411},
  editor =	{Thomas Ball and J\"{u}rgen Giesl and Reiner H\"{a}hnle and Tobias Nipkow},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09411.1},
  URN =		{urn:nbn:de:0030-drops-25032},
  doi =		{10.4230/DagSemProc.09411.1},
  annote =	{Keywords: Formal Logic, Deduction, Artificial Intelligence}
}
Document
09411 Executive Summary – Interaction versus Automation: The two Faces of Deductions

Authors: Thomas Ball, Jürgen Giesl, Reiner Hähnle, and Tobias Nipkow

Published in: Dagstuhl Seminar Proceedings, Volume 9411, Interaction versus Automation: The two Faces of Deduction (2010)


Abstract
This seminar was the ninth in the series of the Dagstuhl "Deduction" seminars held biennially since 1993. Its goal was to bring together the closely related but unnecessarily disjoint communities of researchers working in interactive and automatic program verification.

Cite as

Thomas Ball, Jürgen Giesl, Reiner Hähnle, and Tobias Nipkow. 09411 Executive Summary – Interaction versus Automation: The two Faces of Deductions. In Interaction versus Automation: The two Faces of Deduction. Dagstuhl Seminar Proceedings, Volume 9411, pp. 1-4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)


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@InProceedings{ball_et_al:DagSemProc.09411.2,
  author =	{Ball, Thomas and Giesl, J\"{u}rgen and H\"{a}hnle, Reiner and Nipkow, Tobias},
  title =	{{09411 Executive Summary – Interaction versus Automation: The two Faces of Deductions}},
  booktitle =	{Interaction versus Automation: The two Faces of Deduction},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9411},
  editor =	{Thomas Ball and J\"{u}rgen Giesl and Reiner H\"{a}hnle and Tobias Nipkow},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09411.2},
  URN =		{urn:nbn:de:0030-drops-24213},
  doi =		{10.4230/DagSemProc.09411.2},
  annote =	{Keywords: Formal Logic, Deduction, Artificial Intelligence}
}
Document
Towards a Verified Enumeration of All Tame Plane Graphs

Authors: Tobias Nipkow and Gertrud Bauer

Published in: Dagstuhl Seminar Proceedings, Volume 5021, Mathematics, Algorithms, Proofs (2006)


Abstract
In his proof of the Kepler conjecture, Thomas Hales introduced the notion of tame graphs and provided a Java program for enumerating all tame plane graphs. We have translated his Java program into an executable function in HOL ("the generator"), have formalized the notions of tameness and planarity in HOL, and have partially proved that the generator returns all tame plane graphs. Running the generator in ML has shows that the list of plane tame graphs ("the archive") that Thomas Hales also provides is complete. Once we have finished the completeness proof for the generator. In addition we checked the redundancy of the archive by formalising an executable notion of isomorphism between plane graphs, and checking if the archive contains only graphs produced by the generator. It turned out that 2257 of the 5128 graphs in the archive are either not tame or isomorphic to another graph in the archive.

Cite as

Tobias Nipkow and Gertrud Bauer. Towards a Verified Enumeration of All Tame Plane Graphs. In Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, Volume 5021, pp. 1-25, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{nipkow_et_al:DagSemProc.05021.21,
  author =	{Nipkow, Tobias and Bauer, Gertrud},
  title =	{{Towards a Verified Enumeration of All Tame Plane Graphs}},
  booktitle =	{Mathematics, Algorithms, Proofs},
  pages =	{1--25},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5021},
  editor =	{Thierry Coquand and Henri Lombardi and Marie-Fran\c{c}oise Roy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05021.21},
  URN =		{urn:nbn:de:0030-drops-4343},
  doi =		{10.4230/DagSemProc.05021.21},
  annote =	{Keywords: Kepler conjecture, certified proofs, flyspeck}
}
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