Publications by André Platzer (by area)

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Table of Contents
  1. List of Publications
  2. Logic & Proofs
    1. Logic for Hybrid Systems
    2. Logic for Hybrid Games
    3. Logic for Distributed Hybrid Systems
    4. Logic for Stochastic Hybrid Systems
    5. Logic for Hybrid System Extensions
    6. Discrete Program Logics
    7. Logic & Probability
    8. Proof Theory
    9. Differential Invariants
  3. Model Checking & Checking Models
    1. Model Checking & Statistical Model Checking
    2. Model Safety Transfer & Verified Runtime Validation
  4. Artificial Intelligence
    1. Safe AI / Proofs for AI
    2. AI for Proofs
    3. AI Solvers
  5. Tools
    1. Theorem Provers
    2. Component-based Verification
    3. Compilation
  6. Applications
    1. Verification of Aerospace Systems
    2. Verification of Automotive Systems
    3. Verification of Railway Systems
    4. Verification of Robot Systems
    5. Hybrid Games Logic Applications
  7. Surveys
    1. Technical Surveys
    2. High-Level Surveys
  8. Other
    1. Arithmetic & Computer Algebra
    2. Architecture
    3. Education
Publications
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List of Publications

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Logic & Proofs

Logic for Hybrid Systems

The most canonical papers are the original complete journal article [4], an elegant Hilbert calculus with the complete proof theory [12], and the modern differential-form version of differential dynamic logic [18]. The technical survey from a LICS'12 tutorial [13] is also helpful. The most comprehensive and very readable resource is in the textbook [20].
  1. Yong Kiam Tan, Stefan Mitsch and André Platzer.
    Verifying switched system stability with logic.
    In Ezio Bartocci and Sylvie Putot, editors, Hybrid Systems: Computation and Control (part of CPS Week 2022), HSCC'22. Article No. 2, pp. 1-11. ACM, 2022.
    HSCC Best Paper Award and HSCC Best Repeatability Evaluation Award. © The authors
    [bib | | pdf | doi | slides | video | kyx | arXiv | artifact | abstract]

  2. Yong Kiam Tan and André Platzer.
    Switched systems as hybrid programs.
    In Raphaël M. Jungers, Necmiye Ozay and Alessandro Abate, editors, 7th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2021, volume 54(5) of IFAC-PapersOnline, pp. 247-252. 2021. © The authors
    [bib | | pdf | doi | kyx | arXiv | abstract]

  3. Yong Kiam Tan and André Platzer.
    Deductive stability proofs for ordinary differential equations.
    In Jan Friso Groote and Kim G. Larsen, editors, Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, Proceedings, Part II, volume 12652 of LNCS, pp. 181–199. Springer, 2021. © The authors
    [bib | | pdf | doi | mypdf | slides | video | kyx | arXiv | abstract]

  4. Yong Kiam Tan and André Platzer.
    An axiomatic approach to existence and liveness for differential equations.
    Formal Aspects of Computing 33(4), pp. 461-518, 2021.
    Special issue for selected papers from FM'19. © The authors
    [bib | | pdf | doi | arXiv | FM'19 | abstract]

  5. André Platzer and Yong Kiam Tan.
    Differential equation invariance axiomatization.
    J. ACM 67(1), 6:1-6:66, 2020. © The authors
    [bib | | pdf | doi | mypdf | slides | video | arXiv | abstract]

  6. André Platzer and Yong Kiam Tan.
    Differential equation axiomatization:
       The impressive power of differential ghosts.
    In Anuj Dawar and Erich Grädel, editors, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS'18, pp. 819-828. ACM 2018. © The authors
    [bib | | pdf | doi | mypdf | slides | video | arXiv | JACM'20 | abstract]

  7. André Platzer.
    Logical Foundations of Cyber-Physical Systems.
    Springer, Cham, 2018. 659 pages. ISBN 978-3-319-63587-3.
    [bib | | doi | slides | video | book | web | errata | abstract]

  8. Brandon Bohrer, Vincent Rahli, Ivana Vukotic, Marcus Völp, and André Platzer.
    Formally verified differential dynamic logic.
    Certified Programs and Proofs - 6th ACM SIGPLAN Conference, CPP 2017, Paris, France, January 16-17, 2017, pp. 208-221, ACM, 2017. © ACM
    [bib | | pdf | doi | slides | Isabelle | Coq | abstract]

  9. André Platzer.
    A complete uniform substitution calculus for differential dynamic logic.
    Journal of Automated Reasoning 59(2), pp. 219-265, 2017. © The author
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  10. Sarah M. Loos and André Platzer.
    Differential refinement logic.
    ACM/IEEE Symposium on Logic in Computer Science, LICS 2016, July 5–8, 2016, New York, NY, USA, pp. 505-514. ACM, 2016. © The authors
    [bib | | pdf | doi | mypdf | slides | abstract]

  11. André Platzer.
    A uniform substitution calculus for differential dynamic logic.
    In Amy P. Felty and Aart Middeldorp, editors, International Conference on Automated Deduction, CADE-25, Berlin, Germany, Proceedings, volume 9195 of LNCS, pp. 467-481. Springer, 2015. © Springer
    [bib | | pdf | doi | slides | arXiv | JAR'17 | abstract]

  12. André Platzer.
    Dynamic logics of dynamical systems.
    arXiv:1205.4788, May 2012. Long version of LICS'12 invited tutorial.
    [bib | | pdf | arXiv | LICS'12 | abstract]

  13. André Platzer.
    A differential operator approach to equational differential invariants.
    In Lennart Beringer and Amy Felty, editors, Interactive Theorem Proving, International Conference, ITP 2012, August 13-15, Princeton, USA, Proceedings, volume 7406 of LNCS, pp. 28-48. Springer, 2012. © Springer
    Invited paper.
    [bib | | pdf | doi | slides | abstract]

  14. André Platzer.
    Logics of dynamical systems.
    ACM/IEEE Symposium on Logic in Computer Science, LICS 2012, June 25–28, 2012, Dubrovnik, Croatia, pp. 13-24. IEEE 2012. © IEEE
    Invited paper.
    [bib | | pdf | doi | slides | abstract]

  15. André Platzer.
    The complete proof theory of hybrid systems.
    ACM/IEEE Symposium on Logic in Computer Science, LICS 2012, June 25–28, 2012, Dubrovnik, Croatia, pp. 541-550. IEEE 2012. © IEEE
    [bib | | pdf | doi | slides | TR | abstract]

  16. André Platzer.
    The structure of differential invariants and differential cut elimination.
    Logical Methods in Computer Science 8(4), pp. 1-38, 2012. © The author
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  17. André Platzer.
    Logic and compositional verification of hybrid systems.
    In Ganesh Gopalakrishnan and Shaz Qadeer, editors, Computer Aided Verification, CAV 2011, Snowbird, UT, USA, Proceedings, volume 6806 of LNCS, pp. 28-43. Springer, 2011. © Springer
    Invited tutorial.
    [bib | | pdf | doi | slides | abstract]

  18. André Platzer.
    Logical Analysis of Hybrid Systems:
       Proving Theorems for Complex Dynamics.
    Springer, Heidelberg, 2010. 426 pages. ISBN 978-3-642-14508-7.
    [bib | | doi | book | web | errata | abstract]

  19. André Platzer and Edmund M. Clarke.
    Computing differential invariants of hybrid systems as fixedpoints.
    Formal Methods in System Design 35(1), pp. 98-120, 2009.
    Special issue for selected papers from CAV'08. © Springer
    [bib | | pdf | doi | study | CAV'08 | abstract]

  20. André Platzer.
    Differential Dynamic Logics:
       Automated Theorem Proving for Hybrid Systems.
    PhD Thesis, Department of Computing Science, University of Oldenburg, 2008.
    ACM Doctoral Dissertation Honorable Mention Award in 2009.
    Extended version appeared as book Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics, Springer, 2010.
    [bib | | pdf | eprint | slides | book | ebook | abstract]

  21. André Platzer and Edmund M. Clarke.
    Computing differential invariants of hybrid systems as fixedpoints.
    In Aarti Gupta and Sharad Malik, editors, Computer Aided Verification, CAV 2008, Princeton, USA, Proceedings, volume 5123 of LNCS, pp. 176-189, Springer, 2008. © Springer
    [bib | | pdf | doi | slides | study | TR | FMSD'09 | abstract]

  22. André Platzer.
    Differential-algebraic dynamic logic for differential-algebraic programs.
    Journal of Logic and Computation 20(1), pp. 309-352, 2010.
    Special issue for selected papers from TABLEAUX'07. © The author
    [bib | | pdf | doi | eprint | study | errata | TABLEAUX'07 | abstract]

  23. André Platzer.
    Differential dynamic logic for hybrid systems.
    Journal of Automated Reasoning 41(2), pp. 143-189, 2008. © The author
    [bib | | pdf | doi | mypdf | study | abstract]

  24. André Platzer.
    Differential dynamic logic for verifying parametric hybrid systems.
    In Nicola Olivetti, editor, Automated Reasoning with Analytic Tableaux and Related Methods, International Conference, TABLEAUX 2007, Aix en Provence, France, July 3-6, 2007, Proceedings, volume 4548 of LNCS, pp. 216-232. Springer, 2007. © Springer
    TABLEAUX Best Paper Award.
    [bib | | pdf | doi | slides | study | TR | abstract]

  25. André Platzer.
    Differential logic for reasoning about hybrid systems.
    In Alberto Bemporad, Antonio Bicchi and Giorgio Buttazzo, editors, Hybrid Systems: Computation and Control, 10th International Conference, HSCC 2007, Pisa, Italy, Proceedings, volume 4416 of LNCS, pp. 746-749. Springer, 2007. © Springer
    [bib | | pdf | doi | poster | abstract]

  26. André Platzer.
    Towards a hybrid dynamic logic for hybrid dynamic systems.
    In Patrick Blackburn, Thomas Bolander, Torben Braüner, Valeria de Paiva and Jørgen Villadsen, editors, Proc., International Workshop on Hybrid Logic, HyLo 2006, Seattle, USA, Electr. Notes Theor. Comput. Sci. 174(6):63-77, 2007.
    [bib | | pdf | doi | slides | abstract]

Logic for Hybrid Games

The most important papers are the TOCL'15 article on hybrid games [1] and the TOCL'17 article on differential hybrid games [1]. A very readable introduction is in Part III of the textbook [20].
  1. Brandon Bohrer and André Platzer.
    Refining constructive hybrid games.
    In Zena M. Ariola, editor, 5th International Conference on Formal Structures for Computation and Deduction, FSCD 2020, June 29 - July 5, Paris, France, Proceedings, volume 167 of LIPIcs, pp. 14:1-14:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik 2020. © The authors
    [bib | | pdf | doi | mypdf | slides | arXiv | abstract]

  2. Brandon Bohrer and André Platzer.
    Constructive hybrid games.
    In Nicolas Peltier and Viorica Sofronie-Stokkermans, editors, Automated Reasoning, 10th International Joint Conference, IJCAR 2020, Paris, France, Proceedings, Part I, volume 12166 of LNCS, pp. 454-473. Springer 2020. © The authors
    [bib | | pdf | doi | mypdf | slides | arXiv | abstract]

  3. André Platzer.
    Uniform substitution at one fell swoop.
    In Pascal Fontaine, editor, International Conference on Automated Deduction, CADE-27, Natal, Brazil, Proceedings, volume 11716 of LNCS, pp. 425-441. Springer, 2019. © The author
    [bib | | pdf | doi | mypdf | slides | Isabelle | arXiv | abstract]

  4. André Platzer.
    Uniform substitution for differential game logic.
    In Didier Galmiche, Stephan Schulz and Roberto Sebastiani, editors, Automated Reasoning, 9th International Joint Conference, IJCAR 2018, Oxford, UK, Proceedings, volume 10900 of LNCS, pp. 211-227. Springer 2018. © Springer
    [bib | | pdf | doi | slides | arXiv | abstract]

  5. André Platzer.
    Logical Foundations of Cyber-Physical Systems.
    Springer, Cham, 2018. 659 pages. ISBN 978-3-319-63587-3.
    [bib | | doi | slides | video | book | web | errata | abstract]

  6. André Platzer.
    Differential hybrid games.
    ACM Trans. Comput. Log. 18(3), pp. 19:1-19:44, 2017. © The author
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  7. André Platzer.
    Differential game logic.
    ACM Trans. Comput. Log. 17(1), pp. 1:1-1:52, 2015. © The author
    [bib | | pdf | doi | mypdf | arXiv | errata | abstract]

  8. Jan-David Quesel and André Platzer.
    Playing hybrid games with KeYmaera.
    In Bernhard Gramlich, Dale Miller and Ulrike Sattler, editors, Automated Reasoning, 6th International Joint Conference, IJCAR'12, Manchester, UK, Proceedings, volume 7364 of LNCS, pp. 439-453. Springer, 2012. © Springer
    [bib | | pdf | doi | slides | study | abstract]

  9. André Platzer.
    Differential Game Logic for Hybrid Games.
    School of Computer Science, Carnegie Mellon University, CMU-CS-12-105, March 2012.
    Also see new results.
    [bib | | pdf | TOCL'15 | abstract]

Logic for Distributed Hybrid Systems

The most important paper is the LMCS'12 article [3].
  1. André Platzer.
    Dynamic logics of dynamical systems.
    arXiv:1205.4788, May 2012. Long version of LICS'12 invited tutorial.
    [bib | | pdf | arXiv | LICS'12 | abstract]

  2. André Platzer.
    A complete axiomatization of quantified differential dynamic logic for distributed hybrid systems.
    Logical Methods in Computer Science 8(4), pp. 1-44, 2012.
    Special issue for selected papers from CSL'10. © The author
    [bib | | pdf | doi | arXiv | CSL'10 | abstract]

  3. André Platzer.
    Quantified differential invariants.
    In Emilio Frazzoli and Radu Grosu, editors, Proceedings of the 14th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2011, Chicago, USA, April 12-14, pp. 63-72. ACM, 2011. © ACM
    [bib | | pdf | doi | slides | abstract]

  4. André Platzer.
    Quantified differential dynamic logic for distributed hybrid systems.
    In Anuj Dawar and Helmut Veith, editors, Computer Science Logic, 19th EACSL Annual Conference, CSL 2010, Brno, Czech Republic, August 23-27, 2010. Proceedings, volume 6247 of LNCS, pp. 469-483. Springer, 2010. © Springer
    [bib | | pdf | doi | slides | TR | LMCS'12 | abstract]

Logic for Stochastic Hybrid Systems

  1. André Platzer.
    Dynamic logics of dynamical systems.
    arXiv:1205.4788, May 2012. Long version of LICS'12 invited tutorial.
    [bib | | pdf | arXiv | LICS'12 | abstract]

  2. André Platzer.
    Stochastic differential dynamic logic for stochastic hybrid programs.
    In Nikolaj Bjørner and Viorica Sofronie-Stokkermans, editors, International Conference on Automated Deduction, CADE-23, Wroclaw, Poland, Proceedings, volume 6803 of LNCS, pp. 446-460. Springer, 2011. © Springer
    [bib | | pdf | doi | slides | TR | abstract]

Logic for Hybrid System Extensions

  1. João G. Martins, André Platzer, and João Leite.
    Dynamic doxastic differential dynamic logic for belief-aware cyber-physical systems.
    In Serenella Cerrito and Andrei Popescu, editors, Automated Reasoning with Analytic Tableaux and Related Methods, International Conference, TABLEAUX 2019, London, September 3-5, 2019, Proceedings, volume 11714 of LNCS, pp. 428-445. Springer, 2019. © Springer Nature Switzerland AG
    [bib | | pdf | doi | slides | abstract]

  2. Katherine Cordwell and André Platzer.
    Towards physical hybrid systems.
    In Pascal Fontaine, editor, International Conference on Automated Deduction, CADE-27, Natal, Brazil, Proceedings, volume 11716 of LNCS, pp. 216-232. Springer, 2019. © Springer
    [bib | | pdf | doi | slides | arXiv | abstract]

  3. Brandon Bohrer, Manuel Fernández and André Platzer.
    dLɩ Definite descriptions in differential dynamic logic.
    In Pascal Fontaine, editor, International Conference on Automated Deduction, CADE-27, Natal, Brazil, Proceedings, volume 11716 of LNCS, pp. 94-110. Springer, 2019. © Springer
    [bib | | pdf | doi | slides | TR | abstract]

  4. Brandon Bohrer and André Platzer.
    A hybrid, dynamic logic for hybrid-dynamic information flow.
    In Anuj Dawar and Erich Grädel, editors, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS'18, pp. 115-124. ACM 2018. © The authors. Publication rights licensed to ACM
    [bib | | pdf | doi | slides | TR | abstract]

  5. Jean-Baptiste Jeannin and André Platzer.
    dTL2: Differential temporal dynamic logic with nested temporalities for hybrid systems.
    In Stéphane Demri, Deepak Kapur and Christoph Weidenbach, editors, Automated Reasoning, 7th International Joint Conference, IJCAR 2014, Vienna, Austria, July 19-22, 2014, Proceedings, volume 8562 of LNCS, pp. 292-306. Springer, 2014. © Springer
    [bib | | pdf | doi | slides | abstract]

  6. André Platzer.
    A temporal dynamic logic for verifying hybrid system invariants.
    In Sergei Artemov and Anil Nerode, editors, Logical Foundations of Computer Science, International Symposium, LFCS 2007, New York, USA, Proceedings, volume 4514 of LNCS, pp. 457-471. Springer, 2007. © Springer
    [bib | | pdf | doi | slides | study | TR | abstract]

Discrete Program Logics

  1. Brandon Bohrer and André Platzer.
    Constructive game logic.
    In Peter Müller, editor, Programming Languages and Systems - 29th European Symposium on Programming, ESOP 2020, volume 12075 of LNCS, pp. 84-111. Springer, 2020. © The authors
    [bib | | pdf | doi | mypdf | slides | arXiv | abstract]

  2. Bernhard Beckert and André Platzer.
    Dynamic logic with non-rigid functions:
       A basis for object-oriented program verification.
    In Uli Furbach and Natarajan Shankar, editors, Automated Reasoning, Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006, Proceedings, volume 4130 of LNCS, pp. 266-280. Springer, 2006. © Springer
    [bib | | pdf | doi | slides | abstract]

  3. André Platzer.
    An Object-oriented Dynamic Logic with Updates.
    Master's Thesis, University of Karlsruhe, Department of Computer Science. Institute for Logic, Complexity and Deduction Systems, September 2004.
    Short version appeared as Dynamic logic with non-rigid functions: A basis for object-oriented program verification at IJCAR 2006.
    [bib | | pdf | slides | IJCAR'06 | abstract]

  4. André Platzer.
    Using a Program Verification Calculus for Constructing Specifications from Implementations.
    Minor Thesis (Studienarbeit), University of Karlsruhe, Department of Computer Science. Institute for Logic, Complexity and Deduction Systems, February 2004.
    [bib | | pdf | slides | abstract]

Logic & Probability

  1. Erik P. Zawadzki, André Platzer and Geoffrey J. Gordon.
    A generalization of SAT and #SAT for policy evaluation.
    In Francesca Rossi, editor, IJCAI 2013, Proceedings of the 23nd International Joint Conference on Artificial Intelligence, Beijing, China, August 3-9, 2013, pp. 2583-2589, IJCAI/AAAI, 2013.
    [bib | | pdf | eprint | poster | TR | abstract]

  2. André Platzer.
    Dynamic logics of dynamical systems.
    arXiv:1205.4788, May 2012. Long version of LICS'12 invited tutorial.
    [bib | | pdf | arXiv | LICS'12 | abstract]

  3. André Platzer.
    Stochastic differential dynamic logic for stochastic hybrid programs.
    In Nikolaj Bjørner and Viorica Sofronie-Stokkermans, editors, International Conference on Automated Deduction, CADE-23, Wroclaw, Poland, Proceedings, volume 6803 of LNCS, pp. 446-460. Springer, 2011. © Springer
    [bib | | pdf | doi | slides | TR | abstract]

Proof Theory

  1. André Platzer and Yong Kiam Tan.
    Differential equation invariance axiomatization.
    J. ACM 67(1), 6:1-6:66, 2020. © The authors
    [bib | | pdf | doi | mypdf | slides | video | arXiv | abstract]

  2. André Platzer and Yong Kiam Tan.
    Differential equation axiomatization:
       The impressive power of differential ghosts.
    In Anuj Dawar and Erich Grädel, editors, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS'18, pp. 819-828. ACM 2018. © The authors
    [bib | | pdf | doi | mypdf | slides | video | arXiv | JACM'20 | abstract]

  3. André Platzer.
    Differential hybrid games.
    ACM Trans. Comput. Log. 18(3), pp. 19:1-19:44, 2017. © The author
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  4. André Platzer.
    A complete uniform substitution calculus for differential dynamic logic.
    Journal of Automated Reasoning 59(2), pp. 219-265, 2017. © The author
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  5. André Platzer.
    Differential game logic.
    ACM Trans. Comput. Log. 17(1), pp. 1:1-1:52, 2015. © The author
    [bib | | pdf | doi | mypdf | arXiv | errata | abstract]

  6. André Platzer.
    The complete proof theory of hybrid systems.
    ACM/IEEE Symposium on Logic in Computer Science, LICS 2012, June 25–28, 2012, Dubrovnik, Croatia, pp. 541-550. IEEE 2012. © IEEE
    [bib | | pdf | doi | slides | TR | abstract]

  7. André Platzer.
    The structure of differential invariants and differential cut elimination.
    Logical Methods in Computer Science 8(4), pp. 1-38, 2012. © The author
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  8. André Platzer.
    Logical Analysis of Hybrid Systems:
       Proving Theorems for Complex Dynamics.
    Springer, Heidelberg, 2010. 426 pages. ISBN 978-3-642-14508-7.
    [bib | | doi | book | web | errata | abstract]

  9. André Platzer.
    Differential Dynamic Logics:
       Automated Theorem Proving for Hybrid Systems.
    PhD Thesis, Department of Computing Science, University of Oldenburg, 2008.
    ACM Doctoral Dissertation Honorable Mention Award in 2009.
    Extended version appeared as book Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics, Springer, 2010.
    [bib | | pdf | eprint | slides | book | ebook | abstract]

  10. André Platzer.
    Differential-algebraic dynamic logic for differential-algebraic programs.
    Journal of Logic and Computation 20(1), pp. 309-352, 2010.
    Special issue for selected papers from TABLEAUX'07. © The author
    [bib | | pdf | doi | eprint | study | errata | TABLEAUX'07 | abstract]

  11. André Platzer.
    Differential dynamic logic for hybrid systems.
    Journal of Automated Reasoning 41(2), pp. 143-189, 2008. © The author
    [bib | | pdf | doi | mypdf | study | abstract]

  12. Bernhard Beckert and André Platzer.
    Dynamic logic with non-rigid functions:
       A basis for object-oriented program verification.
    In Uli Furbach and Natarajan Shankar, editors, Automated Reasoning, Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006, Proceedings, volume 4130 of LNCS, pp. 266-280. Springer, 2006. © Springer
    [bib | | pdf | doi | slides | abstract]

  13. André Platzer.
    An Object-oriented Dynamic Logic with Updates.
    Master's Thesis, University of Karlsruhe, Department of Computer Science. Institute for Logic, Complexity and Deduction Systems, September 2004.
    Short version appeared as Dynamic logic with non-rigid functions: A basis for object-oriented program verification at IJCAR 2006.
    [bib | | pdf | slides | IJCAR'06 | abstract]

Differential Invariants

  1. Yong Kiam Tan and André Platzer.
    An axiomatic approach to existence and liveness for differential equations.
    Formal Aspects of Computing 33(4), pp. 461-518, 2021.
    Special issue for selected papers from FM'19. © The authors
    [bib | | pdf | doi | arXiv | FM'19 | abstract]

  2. André Platzer and Yong Kiam Tan.
    Differential equation invariance axiomatization.
    J. ACM 67(1), 6:1-6:66, 2020. © The authors
    [bib | | pdf | doi | mypdf | slides | video | arXiv | abstract]

  3. Yong Kiam Tan and André Platzer.
    An axiomatic approach to liveness for differential equations.
    In Maurice ter Beek, Annabelle McIver, and José N. Oliviera, editors, FM 2019: Formal Methods - The Next 30 Years, volume 11800 of LNCS, pp. 371-388. Springer, 2019. © Springer
    [bib | | pdf | doi | slides | arXiv | FAC'21 | abstract]

  4. Andrew Sogokon, Khalil Ghorbal, Yong Kiam Tan and André Platzer.
    Vector barrier certificates and comparison systems.
    In Klaus Havelund. Bill Roscoe and Jan Peleska, editors, FM 2018: Formal Methods - 22nd International Symposium, Oxford, UK, July 15-17, 2018, Proceedings, volume 10951 of LNCS, pp. 418-437. Springer, 2018. © Springer
    [bib | | pdf | doi | slides | abstract]

  5. André Platzer and Yong Kiam Tan.
    Differential equation axiomatization:
       The impressive power of differential ghosts.
    In Anuj Dawar and Erich Grädel, editors, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS'18, pp. 819-828. ACM 2018. © The authors
    [bib | | pdf | doi | mypdf | slides | video | arXiv | JACM'20 | abstract]

  6. André Platzer.
    A complete uniform substitution calculus for differential dynamic logic.
    Journal of Automated Reasoning 59(2), pp. 219-265, 2017. © The author
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  7. Khalil Ghorbal, Andrew Sogokon, and André Platzer.
    A hierarchy of proof rules for checking positive invariance of algebraic and semi-algebraic sets.
    Computer Languages, Systems & Structures 47(1), pp. 19-43, 2017.
    Special issue for selected papers from VMCAI'15. © Elsevier
    [bib | | pdf | doi | study | VMCAI'15 | abstract]

  8. André Platzer.
    A uniform substitution calculus for differential dynamic logic.
    In Amy P. Felty and Aart Middeldorp, editors, International Conference on Automated Deduction, CADE-25, Berlin, Germany, Proceedings, volume 9195 of LNCS, pp. 467-481. Springer, 2015. © Springer
    [bib | | pdf | doi | slides | arXiv | JAR'17 | abstract]

  9. Khalil Ghorbal, Andrew Sogokon, and André Platzer.
    A hierarchy of proof rules for checking differential invariance of algebraic sets.
    In Deepak D'Souza, Akash Lal, and Kim Guldstrand Larsen, editors, Verification, Model Checking, and Abstract Interpretation - 16th International Conference, VMCAI 2015, Mumbai, India, January 12-14, 2015, Proceedings, volume 8931 of LNCS, pp. 431-448. Springer, 2015. © Springer
    [bib | | pdf | doi | slides | study | ComLan'17 | abstract]

  10. Khalil Ghorbal, Andrew Sogokon, and André Platzer.
    Invariance of conjunctions of polynomial equalities for algebraic differential equations.
    In Markus Müller-Olm and Helmut Seidl, editors, 21st International Static Analysis Symposium, SAS 2014, volume 8723 of LNCS, pp. 151-167. Springer, 2014. © Springer
    [bib | | pdf | doi | slides | study | abstract]

  11. Khalil Ghorbal and André Platzer.
    Characterizing algebraic invariants by differential radical invariants.
    In Erika Ábrahám and Klaus Havelund, editors, Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2014, Proceedings, volume 8413 of LNCS, pp. 279-294. Springer, 2014. © Springer
    [bib | | pdf | doi | slides | study | TR | abstract]

  12. André Platzer.
    Dynamic logics of dynamical systems.
    arXiv:1205.4788, May 2012. Long version of LICS'12 invited tutorial.
    [bib | | pdf | arXiv | LICS'12 | abstract]

  13. André Platzer.
    A differential operator approach to equational differential invariants.
    In Lennart Beringer and Amy Felty, editors, Interactive Theorem Proving, International Conference, ITP 2012, August 13-15, Princeton, USA, Proceedings, volume 7406 of LNCS, pp. 28-48. Springer, 2012. © Springer
    Invited paper.
    [bib | | pdf | doi | slides | abstract]

  14. André Platzer.
    Logics of dynamical systems.
    ACM/IEEE Symposium on Logic in Computer Science, LICS 2012, June 25–28, 2012, Dubrovnik, Croatia, pp. 13-24. IEEE 2012. © IEEE
    Invited paper.
    [bib | | pdf | doi | slides | abstract]

  15. André Platzer.
    The structure of differential invariants and differential cut elimination.
    Logical Methods in Computer Science 8(4), pp. 1-38, 2012. © The author
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  16. André Platzer.
    Logical Analysis of Hybrid Systems:
       Proving Theorems for Complex Dynamics.
    Springer, Heidelberg, 2010. 426 pages. ISBN 978-3-642-14508-7.
    [bib | | doi | book | web | errata | abstract]

  17. André Platzer and Edmund M. Clarke.
    Computing differential invariants of hybrid systems as fixedpoints.
    Formal Methods in System Design 35(1), pp. 98-120, 2009.
    Special issue for selected papers from CAV'08. © Springer
    [bib | | pdf | doi | study | CAV'08 | abstract]

  18. André Platzer.
    Differential Dynamic Logics:
       Automated Theorem Proving for Hybrid Systems.
    PhD Thesis, Department of Computing Science, University of Oldenburg, 2008.
    ACM Doctoral Dissertation Honorable Mention Award in 2009.
    Extended version appeared as book Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics, Springer, 2010.
    [bib | | pdf | eprint | slides | book | ebook | abstract]

  19. André Platzer and Edmund M. Clarke.
    Computing differential invariants of hybrid systems as fixedpoints.
    In Aarti Gupta and Sharad Malik, editors, Computer Aided Verification, CAV 2008, Princeton, USA, Proceedings, volume 5123 of LNCS, pp. 176-189, Springer, 2008. © Springer
    [bib | | pdf | doi | slides | study | TR | FMSD'09 | abstract]

  20. André Platzer.
    Differential-algebraic dynamic logic for differential-algebraic programs.
    Journal of Logic and Computation 20(1), pp. 309-352, 2010.
    Special issue for selected papers from TABLEAUX'07. © The author
    [bib | | pdf | doi | eprint | study | errata | TABLEAUX'07 | abstract]

Model Checking & Checking Models

Model Checking & Statistical Model Checking

  1. Laurent Doyen, Goran Frehse, George J. Pappas, and André Platzer.
    Verification of hybrid systems.
    In Edmund M. Clarke and Thomas A. Henzinger, Helmut Veith, and Roderick Bloem, editors, Handbook of Model Checking, pp. 1047-1110. Springer, 2018. © Springer
    [bib | | pdf | doi | book | abstract]

  2. Paolo Zuliani, André Platzer and Edmund M. Clarke.
    Bayesian statistical model checking with application to Simulink/Stateflow verification.
    Formal Methods in System Design 43(2), pp. 338-367, 2013.
    Special issue on Probabilistic Model Checking. © Springer
    [bib | | pdf | doi | abstract]

  3. David Henriques, João G. Martins, Paolo Zuliani, André Platzer and Edmund M. Clarke.
    Statistical model checking for Markov decision processes.
    In 9th International Conference on Quantitative Evaluation of Systems, QEST 2012, September 17-20, London, UK, pp. 84-93. IEEE Computer Society, 2012. © IEEE
    [bib | | pdf | doi | slides | study | abstract]

  4. João G. Martins, André Platzer and João Leite.
    Statistical model checking for distributed probabilistic control hybrid automata with smart grid applications.
    In Shengchao Qin and Zongyan Qiu, editors, International Conference on Formal Engineering Methods, ICFEM'11, Durham, UK, Proceedings, volume 6991 of LNCS, pp. 131-146. Springer, 2011. © Springer
    [bib | | pdf | doi | slides | study | abstract]

  5. Paolo Zuliani, André Platzer and Edmund M. Clarke.
    Bayesian statistical model checking with application to Simulink/Stateflow verification.
    In Karl Henrik Johansson and Wang Yi, editors, Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2010, Stockholm, Sweden, April 12-15, pp. 243-252. ACM, 2010. © ACM
    [bib | | pdf | doi | slides | TR | abstract]

  6. Sumit Kumar Jha, Edmund Clarke, Christopher Langmead, Axel Legay, André Platzer and Paolo Zuliani.
    A Bayesian approach to model checking biological systems.
    In Pierpaolo Degano and Roberto Gorrieri, editors, Computational Methods in Systems Biology, 7th International Conference, CMSB 2009, Bologna, Italy, Proceedings, volume 5688 of LNCS, pp. 218-234. Springer, 2009. © Springer
    [bib | | pdf | doi | TR | abstract]

  7. André Platzer and Edmund M. Clarke.
    The image computation problem in hybrid systems model checking.
    In Alberto Bemporad, Antonio Bicchi and Giorgio Buttazzo, editors, Hybrid Systems: Computation and Control, 10th International Conference, HSCC 2007, Pisa, Italy, Proceedings, volume 4416 of LNCS, pp. 473-486. Springer, 2007, © Springer
    [bib | | pdf | doi | slides | tool | abstract]

  8. Stephanie Kemper and André Platzer.
    SAT-based abstraction refinement for real-time systems.
    In Frank S. de Boer and Vladimir Mencl, editors, Formal Aspects of Component Software, Third International Workshop, FACS 2006, Prague, Czech Republic, Proceedings, Electr. Notes Theor. Comput. Sci., 182:107-122, 2007
    [bib | | pdf | doi | slides | tool | abstract]

Model Safety Transfer & Verified Runtime Validation

  1. Brandon Bohrer, Yong Kiam Tan, Stefan Mitsch, Magnus O. Myreen and André Platzer.
    VeriPhy: Verified controller executables from verified cyber-physical system models.
    In Dan Grossmann, editor, Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2018, pp. 617-630. ACM 2018. © The authors
    [bib | | pdf | doi | mypdf | slides | video | abstract]

  2. Stefan Mitsch and André Platzer.
    ModelPlex: Verified runtime validation of verified cyber-physical system models.
    Formal Methods in System Design 49(1), pp. 33-74. 2016.
    Special issue for selected papers from RV'14. © The authors
    [bib | | pdf | doi | mypdf | RV'14 | abstract]

  3. Stefan Mitsch and André Platzer.
    ModelPlex: Verified runtime validation of verified cyber-physical system models.
    In Borzoo Bonakdarpour and Scott A. Smolka, editors, Runtime Verification - 5th International Conference, RV 2014, Toronto, ON, Canada, September 22-25, 2014. Proceedings, volume 8734 of LNCS, pp. 199-214. Springer, 2014. © Springer
    Best paper finalist
    [bib | | pdf | doi | slides | study | TR | FMSD'16 | abstract]

Artificial Intelligence

Safe AI / Proofs for AI

  1. André Platzer.
    The logical path to autonomous cyber-physical systems.
    In David Parker and Verena Wolf, editors, International Conference on Quantitative Evaluation of SysTems, QEST 2019, Glasgow, UK, Proceedings, volume 11785 of LNCS, pp. 25-33. Springer, 2019. © Springer
    Invited paper.
    [bib | | pdf | doi | slides | abstract]

  2. Nathan Fulton and André Platzer.
    Verifiably safe off-model reinforcement learning.
    In Tomas Vojnar and Lijun Zhang, editors, Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2019, Proceedings, Part I, volume 11427 of LNCS, pp. 413-430. Springer, 2019. © The authors
    [bib | | pdf | doi | arXiv | abstract]

  3. Nathan Fulton and André Platzer.
    Safe AI for CPS.
    In International Testing Conference ITC'18, IEEE, 2018. © IEEE
    Invited paper.
    [bib | | pdf | doi | slides | abstract]

  4. Nathan Fulton and André Platzer.
    Safe reinforcement learning via formal methods:
       Toward safe control through proof and learning.
    In Sheila A. McIlraith and Kilian Q. Weinberger, editors, AAAI Conference on Artificial Intelligence, pp. 6485-6492. AAAI 2018. © AAAI Press
    [bib | | pdf | eprint | slides | abstract]

AI for Proofs

  1. Jonathan Laurent and André Platzer.
    Learning to find proofs and theorems by learning to refine search strategies:
       The case of loop invariant synthesis.
    In Sanmi Koyejo, Shakir Mohamed, Alekh Agarwal, Danielle Belgrave, Kyunghyun Cho and Alice Oh, editors, Advances in Neural Information Processing Systems 35 NeurIPS 2022 pp. 4843–4856.
    [bib | | pdf | eprint | slides | video | poster | arXiv | abstract]

AI Solvers

  1. Erik P. Zawadzki, André Platzer and Geoffrey J. Gordon.
    A generalization of SAT and #SAT for policy evaluation.
    In Francesca Rossi, editor, IJCAI 2013, Proceedings of the 23nd International Joint Conference on Artificial Intelligence, Beijing, China, August 3-9, 2013, pp. 2583-2589, IJCAI/AAAI, 2013.
    [bib | | pdf | eprint | poster | TR | abstract]

  2. Erik P. Zawadzki, Geoffrey J. Gordon and André Platzer.
    An Instantiation-Based Theorem Prover for First-Order Programming.
    In 14th International Conference on Artificial Intelligence and Statistics (AISTATS) 2011, Fort Lauderdale, FL, USA, Proceedings, volume 15 of JMLR W&CP, pp. 855-863, 2011.
    [bib | | pdf | poster | proceedings | abstract]

Tools

Theorem Provers

  1. James Gallicchio, Yong Kiam Tan, Stefan Mitsch and André Platzer.
    Implicit definitions with differential equations for KeYmaera X (System Description).
    In Jasmin Blanchette, Laura Kovacs and Dirk Pattinson, editors, Automated Reasoning, International Joint Conference, IJCAR 2022, Haifa, Israel, August 7-12, 2022, Proceedings. volume 13385 of LNCS, pp. 723-733. Springer, 2022. © The authors
    [bib | | pdf | doi | slides | arXiv | abstract]

  2. Brandon Bohrer and André Platzer.
    Structured proofs for adversarial cyber-physical systems.
    ACM Trans. Embed. Comput. Syst. 20(5s), pp. 93:1-93:26, 2021.
    Special issue on EMSOFT 2021. © The authors
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  3. Andrew Sogokon, Stefan Mitsch, Yong Kiam Tan, Katherine Cordwell and André Platzer.
    Pegasus: Sound continuous invariant generation.
    Formal Methods in System Design 58(1), pp. 5-41, 2022.
    Special issue for selected papers from FM'19. © The authors
    [bib | | pdf | doi | tool | arXiv | FM'19 | abstract]

  4. Stefan Mitsch and André Platzer.
    A Retrospective on Developing Hybrid System Provers in the KeYmaera Family:
       A Tale of Three Provers.
    In Wolfgang Ahrendt et al., editors, Deductive Software Verification: Future Perspectives, volume 12345 of LNCS, pp. 21-64. Springer, 2020. © Springer
    [bib | | pdf | doi | abstract]

  5. Andrew Sogokon, Stefan Mitsch, Yong Kiam Tan, Katherine Cordwell and André Platzer.
    Pegasus: A framework for sound continuous invariant generation.
    In Maurice ter Beek, Annabelle McIver, and José N. Oliviera, editors, FM 2019: Formal Methods - The Next 30 Years, volume 11800 of LNCS, pp. 138-157. Springer, 2019. © Springer
    FM Best Tool Paper Award.
    [bib | | pdf | doi | slides | tool | FMSD | abstract]

  6. Nathan Fulton, Stefan Mitsch, Brandon Bohrer and André Platzer.
    Bellerophon: Tactical theorem proving for hybrid systems.
    In Mauricio Ayala-Rincón and César A. Muñoz, editors, Interactive Theorem Proving, International Conference, ITP 2017, volume 10499 of LNCS, pp. 207-224. Springer, 2017. © Springer
    [bib | | pdf | doi | slides | kyx | abstract]

  7. Nathan Fulton, Stefan Mitsch, Jan-David Quesel, Marcus Völp and André Platzer.
    KeYmaera X: An aXiomatic tactical theorem prover for hybrid systems.
    In Amy P. Felty and Aart Middeldorp, editors, International Conference on Automated Deduction, CADE-25, Berlin, Germany, Proceedings, volume 9195 of LNCS, pp. 527-538. Springer, 2015. © Springer
    [bib | | pdf | doi | slides | poster | tool | abstract]

  8. David W. Renshaw, Sarah M. Loos and André Platzer.
    Distributed theorem proving for distributed hybrid systems.
    In Shengchao Qin and Zongyan Qiu, editors, International Conference on Formal Engineering Methods, ICFEM'11, Durham, UK, Proceedings, volume 6991 of LNCS, pp. 356-371. Springer, 2011. © Springer
    [bib | | pdf | doi | tool | study | errata | abstract]

  9. André Platzer and Jan-David Quesel.
    KeYmaera: A hybrid theorem prover for hybrid systems.
    In Alessandro Armando, Peter Baumgartner and Gilles Dowek, editors, Automated Reasoning, Fourth International Joint Conference, IJCAR 2008, Sydney, Australia, Proceedings, volume 5195 of LNCS, pp. 171-178. Springer, 2008. © Springer
    [bib | | pdf | doi | slides | tool | abstract]

Component-based Verification

  1. Andreas Müller, Stefan Mitsch, Wieland Schwinger and André Platzer.
    A component-based hybrid systems verification and implementation tool in KeYmaera X.
    In Roger Chamberlain, Walid Taha and Martin Törngren, editors, CyPhy 2018, WESE 2018: Cyber Physical Systems. Model-Based Design, revised selected papers, volume 11615 of LNCS, pp. 91-110. Springer, 2019. © Springer
    [bib | | pdf | doi | abstract]

  2. Andreas Müller, Stefan Mitsch, Werner Retschitzegger, Wieland Schwinger and André Platzer.
    Tactical contract composition for hybrid system component verification.
    STTT 20(6), pp. 615-643, 2018.
    Special issue for selected papers from FASE'17. © The authors
    [bib | | pdf | doi | mypdf | study | FASE'17 | abstract]

  3. Brandon Bohrer, Adriel Luo, Xue An Chuang and André Platzer.
    CoasterX: A case study in component-driven hybrid systems proof automation.
    In Maurice Heemels and Antoine Girard, editors, 6th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2018, volume 51(6) of IFAC-PapersOnline, pp. 55-60, 2018. © IFAC
    [bib | | pdf | doi | slides | abstract]

  4. Andreas Müller, Stefan Mitsch, Werner Retschitzegger, Wieland Schwinger and André Platzer.
    Change and delay contracts for hybrid system component verification.
    In Marieke Huisman and Julia Rubin, editors, Fundamental Approaches to Software Engineering. FASE 2017, volume 10202 of LNCS, pp. 134-151. Springer, 2017. © Springer
    [bib | | pdf | doi | slides | study | STTT'18 | abstract]

  5. Andreas Müller, Stefan Mitsch, Werner Retschitzegger, Wieland Schwinger and André Platzer.
    A component-based approach to hybrid systems safety verification.
    In Erika Abraham and Marieke Huisman, editors, Integrated Formal Methods - 12th International Conference, iFM 2016, Reykjavik, Iceland, June 1-4, 2016, Proceedings, volume 9681 of LNCS, pp. 441-456. Springer, 2016. © Springer
    [bib | | pdf | doi | slides | TR | abstract]

  6. Andreas Müller and Stefan Mitsch and André Platzer.
    Verified traffic networks: Component-based verification of cyber-physical flow systems.
    In Intelligent Transportation Systems (ITSC), 2015 IEEE 18th International Conference on, pp. 757-764, 2015. © IEEE
    [bib | | pdf | doi | slides | abstract]

Compilation

  1. Luis Garcia, Stefan Mitsch and André Platzer.
    HyPLC: Hybrid programmable logic controller program translation for verification.
    In Linda Bushnell and Miroslav Pajic, editors, 10th ACM/IEEE International Conference on Cyber-Physical Systems ICCPS, pp. 47-56. 2019. © ACM
    Best paper finalist
    [bib | | pdf | doi | tool | arXiv | abstract]

  2. Brandon Bohrer, Yong Kiam Tan, Stefan Mitsch, Magnus O. Myreen and André Platzer.
    VeriPhy: Verified controller executables from verified cyber-physical system models.
    In Dan Grossmann, editor, Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2018, pp. 617-630. ACM 2018. © The authors
    [bib | | pdf | doi | mypdf | slides | video | abstract]

Applications

Verification of Aerospace Systems

  1. Rachel Cleveland, Stefan Mitsch and André Platzer.
    Formally verified next-generation airborne collision avoidance games in ACAS X.
    ACM Trans. Embed. Comput. Syst. 22(1), pp. 10:1-10:30, 2023. © The authors
    [bib | | pdf | doi | mypdf | kyx | arXiv | abstract]

  2. Jean-Baptiste Jeannin, Khalil Ghorbal, Yanni Kouskoulas, Aurora Schmidt, Ryan Gardner, Stefan Mitsch, and André Platzer.
    A formally verified hybrid system for safe advisories in the next-generation airborne collision avoidance system.
    STTT 19(6), pp. 717-741, 2017.
    Special issue for selected papers from TACAS'15. © Springer
    [bib | | pdf | doi | kyx | study | TACAS'15 | abstract]

  3. Jean-Baptiste Jeannin, Khalil Ghorbal, Yanni Kouskoulas, Ryan Gardner, Aurora Schmidt, Erik Zawadzki, and André Platzer.
    Formal verification of ACAS X, an industrial airborne collision avoidance system.
    In Alain Girault and Nan Guan, editors, International Conference on Embedded Software, EMSOFT'15, Amsterdam, The Netherlands, Proceedings, pp. 127-136. IEEE Press, 2015. © IEEE
    [bib | | pdf | doi | abstract]

  4. Jean-Baptiste Jeannin, Khalil Ghorbal, Yanni Kouskoulas, Ryan Gardner, Aurora Schmidt, Erik Zawadzki, and André Platzer.
    A formally verified hybrid system for the next-generation airborne collision avoidance system.
    In Christel Baier and Cesare Tinelli, editors, Tools and Algorithms for the Construction and Analysis of Systems - 21st International Conference, TACAS 2015, London, UK, April 11-18, 2015, Proceedings, volume 9035 of LNCS, pp. 21-36. Springer, 2015. © Springer
    [bib | | pdf | doi | study | TR | STTT'17 | abstract]

  5. Khalil Ghorbal, Jean-Baptiste Jeannin, Erik P. Zawadzki, André Platzer, Geoffrey J. Gordon, and Peter Capell.
    Hybrid theorem proving of aerospace systems: Applications and challenges.
    Journal of Aerospace Information Systems 11(10), pp. 702-713. 2014.
    Special issue on Software Challenges in Aerospace. © The authors
    [bib | | pdf | doi | abstract]

  6. Sarah M. Loos, David W. Renshaw and André Platzer.
    Formal verification of distributed aircraft controllers.
    In Calin Belta and Franjo Ivancic, editors, Hybrid Systems: Computation and Control (part of CPS Week 2013), HSCC'13, Philadelphia, PA, USA, April 8-13, 2013, pp. 125-130. ACM, 2013. © ACM
    [bib | | pdf | doi | slides | poster | study | TR | abstract]

  7. André Platzer.
    Quantified differential invariants.
    In Emilio Frazzoli and Radu Grosu, editors, Proceedings of the 14th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2011, Chicago, USA, April 12-14, pp. 63-72. ACM, 2011. © ACM
    [bib | | pdf | doi | slides | abstract]

  8. André Platzer.
    Logical Analysis of Hybrid Systems:
       Proving Theorems for Complex Dynamics.
    Springer, Heidelberg, 2010. 426 pages. ISBN 978-3-642-14508-7.
    [bib | | doi | book | web | errata | abstract]

  9. André Platzer and Edmund M. Clarke.
    Formal verification of curved flight collision avoidance maneuvers: A case study.
    In Ana Cavalcanti and Dennis Dams, editors, 16th International Symposium on Formal Methods, FM, Eindhoven, Netherlands, Proceedings, volume 5850 of LNCS, pp. 547-562. Springer, 2009. © Springer
    FM Best Paper Award.
    [bib | | pdf | doi | slides | study | TR | abstract]

  10. André Platzer.
    Differential Dynamic Logics:
       Automated Theorem Proving for Hybrid Systems.
    PhD Thesis, Department of Computing Science, University of Oldenburg, 2008.
    ACM Doctoral Dissertation Honorable Mention Award in 2009.
    Extended version appeared as book Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics, Springer, 2010.
    [bib | | pdf | eprint | slides | book | ebook | abstract]

  11. André Platzer and Edmund M. Clarke.
    Computing differential invariants of hybrid systems as fixedpoints.
    Formal Methods in System Design 35(1), pp. 98-120, 2009.
    Special issue for selected papers from CAV'08. © Springer
    [bib | | pdf | doi | study | CAV'08 | abstract]

  12. André Platzer and Edmund M. Clarke.
    Computing differential invariants of hybrid systems as fixedpoints.
    In Aarti Gupta and Sharad Malik, editors, Computer Aided Verification, CAV 2008, Princeton, USA, Proceedings, volume 5123 of LNCS, pp. 176-189, Springer, 2008. © Springer
    [bib | | pdf | doi | slides | study | TR | FMSD'09 | abstract]

  13. André Platzer.
    Differential-algebraic dynamic logic for differential-algebraic programs.
    Journal of Logic and Computation 20(1), pp. 309-352, 2010.
    Special issue for selected papers from TABLEAUX'07. © The author
    [bib | | pdf | doi | eprint | study | errata | TABLEAUX'07 | abstract]

Verification of Automotive Systems

  1. Andreas Müller, Stefan Mitsch, Werner Retschitzegger, Wieland Schwinger and André Platzer.
    A component-based approach to hybrid systems safety verification.
    In Erika Abraham and Marieke Huisman, editors, Integrated Formal Methods - 12th International Conference, iFM 2016, Reykjavik, Iceland, June 1-4, 2016, Proceedings, volume 9681 of LNCS, pp. 441-456. Springer, 2016. © Springer
    [bib | | pdf | doi | slides | TR | abstract]

  2. Andreas Müller and Stefan Mitsch and André Platzer.
    Verified traffic networks: Component-based verification of cyber-physical flow systems.
    In Intelligent Transportation Systems (ITSC), 2015 IEEE 18th International Conference on, pp. 757-764, 2015. © IEEE
    [bib | | pdf | doi | slides | abstract]

  3. Sarah M. Loos, David Witmer, Peter Steenkiste and André Platzer.
    Efficiency analysis of formally verified adaptive cruise controllers.
    In Andreas Hegyi and Bart De Schutter, editors, 16th International IEEE Conference on Intelligent Transportation Systems, ITSC'13, The Hague, Netherlands, Proceedings, 2013. © IEEE
    [bib | | pdf | doi | slides | study | abstract]

  4. Nikos Aréchiga, Sarah M. Loos, André Platzer and Bruce H. Krogh.
    Using theorem provers to guarantee closed-loop system properties.
    In Dawn Tilbury, editor, American Control Conference, ACC, Montréal, Canada, June 27-29. pp. 3573-3580. 2012. © IEEE
    [bib | | pdf | doi | abstract]

  5. Stefan Mitsch, Sarah M. Loos and André Platzer.
    Towards formal verification of freeway traffic control.
    In Chenyang Lu, editor, ACM/IEEE Third International Conference on Cyber-Physical Systems ICCPS, Beijing, China, April 17-19. pp. 171-180, IEEE. 2012. © IEEE
    [bib | | pdf | doi | slides | study | abstract]

  6. Sarah M. Loos and André Platzer.
    Safe intersections: At the crossing of hybrid systems and verification.
    In Kyongsu Yi, editor, 14th International IEEE Conference on Intelligent Transportation Systems, ITSC'11, Washington, DC, USA, Proceedings, pp. 1181-1186. 2011. © IEEE
    [bib | | pdf | doi | slides | study | abstract]

  7. Sarah M. Loos, André Platzer and Ligia Nistor.
    Adaptive cruise control:
       Hybrid, distributed, and now formally verified.
    In Michael Butler and Wolfram Schulte, editors, 17th International Symposium on Formal Methods, FM, Limerick, Ireland, Proceedings, volume 6664 of LNCS, pp. 42-56. Springer, 2011. © Springer
    [bib | | pdf | doi | slides | study | TR | abstract]

  8. Paolo Zuliani, André Platzer and Edmund M. Clarke.
    Bayesian statistical model checking with application to Simulink/Stateflow verification.
    In Karl Henrik Johansson and Wang Yi, editors, Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2010, Stockholm, Sweden, April 12-15, pp. 243-252. ACM, 2010. © ACM
    [bib | | pdf | doi | slides | TR | abstract]

  9. André Platzer and Edmund M. Clarke.
    Computing differential invariants of hybrid systems as fixedpoints.
    Formal Methods in System Design 35(1), pp. 98-120, 2009.
    Special issue for selected papers from CAV'08. © Springer
    [bib | | pdf | doi | study | CAV'08 | abstract]

  10. André Platzer.
    Differential Dynamic Logics:
       Automated Theorem Proving for Hybrid Systems.
    PhD Thesis, Department of Computing Science, University of Oldenburg, 2008.
    ACM Doctoral Dissertation Honorable Mention Award in 2009.
    Extended version appeared as book Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics, Springer, 2010.
    [bib | | pdf | eprint | slides | book | ebook | abstract]

Verification of Railway Systems

  1. Aditi Kabra, Stefan Mitsch and André Platzer.
    Verified train controllers for the Federal Railroad Administration train kinematics model: Balancing competing brake and track forces.
    IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 41(11), pp. 4409-4420, 2022. Special issue for EMSOFT 2022. © IEEE
    Best paper finalist
    [bib | | doi | slides | video | kyx | extra | abstract]

  2. Brandon Bohrer, Adriel Luo, Xue An Chuang and André Platzer.
    CoasterX: A case study in component-driven hybrid systems proof automation.
    In Maurice Heemels and Antoine Girard, editors, 6th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2018, volume 51(6) of IFAC-PapersOnline, pp. 55-60, 2018. © IFAC
    [bib | | pdf | doi | slides | abstract]

  3. Stefan Mitsch, Marco Gario, Christof J. Budnik, Michael Golm and André Platzer.
    Formal verification of train control with air pressure brakes.
    In Alessandro Fantechi, Thierry Lecomte and Alexander Romanovsky, editors, RSSRail 2017: Reliability, Safety, and Security of Railway Systems, volume 10598 of LNCS, pp. 173-191. Springer, 2017. © Springer
    [bib | | pdf | doi | slides | abstract]

  4. André Platzer.
    Logical Analysis of Hybrid Systems:
       Proving Theorems for Complex Dynamics.
    Springer, Heidelberg, 2010. 426 pages. ISBN 978-3-642-14508-7.
    [bib | | doi | book | web | errata | abstract]

  5. André Platzer and Jan-David Quesel.
    European Train Control System: A case study in formal verification.
    In Karin Breitman and Ana Cavalcanti, editors, 11th International Conference on Formal Engineering Methods, ICFEM, Rio de Janeiro, Brasil, Proceedings, volume 5885 of LNCS, pp. 246-265. Springer, 2009. © Springer
    [bib | | pdf | doi | slides | kyx | TR | old | abstract]

  6. André Platzer.
    Differential Dynamic Logics:
       Automated Theorem Proving for Hybrid Systems.
    PhD Thesis, Department of Computing Science, University of Oldenburg, 2008.
    ACM Doctoral Dissertation Honorable Mention Award in 2009.
    Extended version appeared as book Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics, Springer, 2010.
    [bib | | pdf | eprint | slides | book | ebook | abstract]

  7. André Platzer and Jan-David Quesel.
    Logical verification and systematic parametric analysis in train control.
    In Magnus Egerstedt and Bud Mishra, editors, Hybrid Systems: Computation and Control, 11th International Conference, HSCC 2008, St. Louis, USA, Proceedings, volume 4981 of LNCS, pp. 646-649. Springer, 2008. © Springer
    [bib | | pdf | doi | poster | abstract]

  8. André Platzer.
    Differential dynamic logic for hybrid systems.
    Journal of Automated Reasoning 41(2), pp. 143-189, 2008. © The author
    [bib | | pdf | doi | mypdf | study | abstract]

  9. Werner Damm, Alfred Mikschl, Jens Oehlerking, Ernst-Rüdiger Olderog, Jun Pang, André Platzer, Marc Segelken and Boris Wirtz.
    Automating verification of cooperation, control, and design in traffic applications.
    In Cliff Jones, Zhiming Liu and Jim Woodcock, editors, Formal Methods and Hybrid Real-Time Systems, volume 4700 of LNCS, pp. 115-169. Springer, 2007. © Springer
    Invited paper.
    [bib | | pdf | doi | abstract]

  10. André Platzer.
    Differential dynamic logic for verifying parametric hybrid systems.
    In Nicola Olivetti, editor, Automated Reasoning with Analytic Tableaux and Related Methods, International Conference, TABLEAUX 2007, Aix en Provence, France, July 3-6, 2007, Proceedings, volume 4548 of LNCS, pp. 216-232. Springer, 2007. © Springer
    TABLEAUX Best Paper Award.
    [bib | | pdf | doi | slides | study | TR | abstract]

Verification of Robot Systems

  1. Qin Lin, Stefan Mitsch, André Platzer and John M. Dolan.
    Safe and resilient practical waypoint-following for autonomous vehicles.
    IEEE Control Syst. Lett. 6, pp. 1574-1579, 2022. © IEEE
    [bib | | pdf | doi | abstract]

  2. Brandon Bohrer, Yong Kiam Tan, Stefan Mitsch, Andrew Sogokon and André Platzer.
    A formal safety net for waypoint following in ground robots.
    IEEE Robotics and Automation Letters 4(3), pp. 2910-2917, 2019. © IEEE
    [bib | | pdf | doi | kyx | study | arXiv | abstract]

  3. Stefan Mitsch, Khalil Ghorbal, David Vogelbacher, and André Platzer.
    Formal verification of obstacle avoidance and navigation of ground robots.
    International Journal of Robotics Research 36(12), pp. 1312-1340, 2017. © The authors
    [bib | | pdf | doi | kyx | arXiv | abstract]

  4. Stefan Mitsch, Khalil Ghorbal and André Platzer.
    On provably safe obstacle avoidance for autonomous robotic ground vehicles.
    In Paul Newman, Dieter Fox, and David Hsu, editors, Robotics: Science and Systems, RSS, 2013. © The author
    [bib | | pdf | eprint | slides | video | study | IJRR'17 | abstract]

  5. Yanni Kouskoulas, André Platzer and Peter Kazanzides.
    Formal Methods for Robotic System Control Software.
    Johns Hopkins APL Technical Digest 32(2), pp. 490-498, 2013.
    [bib | | pdf | abstract]

  6. Yanni Kouskoulas, David W. Renshaw, André Platzer and Peter Kazanzides.
    Certifying the safe design of a virtual fixture control algorithm for a surgical robot.
    In Calin Belta and Franjo Ivancic, editors, Hybrid Systems: Computation and Control (part of CPS Week 2013), HSCC'13, Philadelphia, PA, USA, April 8-13, 2013, pp. 263-272. ACM, 2013. © ACM
    [bib | | pdf | doi | slides | study | abstract]

Hybrid Games Logic Applications

Differential game logic [1] [1] has a number of different applications.
  1. Brandon Bohrer and André Platzer.
    Structured proofs for adversarial cyber-physical systems.
    ACM Trans. Embed. Comput. Syst. 20(5s), pp. 93:1-93:26, 2021.
    Special issue on EMSOFT 2021. © The authors
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  2. Rachel Cleveland, Stefan Mitsch and André Platzer.
    Formally verified next-generation airborne collision avoidance games in ACAS X.
    ACM Trans. Embed. Comput. Syst. 22(1), pp. 10:1-10:30, 2023. © The authors
    [bib | | pdf | doi | mypdf | kyx | arXiv | abstract]

  3. Brandon Bohrer and André Platzer.
    Structured proofs for adversarial cyber-physical systems.
    ACM Trans. Embed. Comput. Syst. 20(5s), pp. 93:1-93:26, 2021.
    Special issue on EMSOFT 2021. © The authors
    [bib | | pdf | doi | mypdf | arXiv | abstract]

  4. Brandon Bohrer and André Platzer.
    Refining constructive hybrid games.
    In Zena M. Ariola, editor, 5th International Conference on Formal Structures for Computation and Deduction, FSCD 2020, June 29 - July 5, Paris, France, Proceedings, volume 167 of LIPIcs, pp. 14:1-14:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik 2020. © The authors
    [bib | | pdf | doi | mypdf | slides | arXiv | abstract]

Surveys

Technical Surveys

The best and most succinct technical survey with many important aspects is from an invited tutorial at LICS'12 [13]. More comprehensive information can be found in the book [9] and textbook [20].
  1. Stefan Mitsch and André Platzer.
    A Retrospective on Developing Hybrid System Provers in the KeYmaera Family:
       A Tale of Three Provers.
    In Wolfgang Ahrendt et al., editors, Deductive Software Verification: Future Perspectives, volume 12345 of LNCS, pp. 21-64. Springer, 2020. © Springer
    [bib | | pdf | doi | abstract]

  2. Laurent Doyen, Goran Frehse, George J. Pappas, and André Platzer.
    Verification of hybrid systems.
    In Edmund M. Clarke and Thomas A. Henzinger, Helmut Veith, and Roderick Bloem, editors, Handbook of Model Checking, pp. 1047-1110. Springer, 2018. © Springer
    [bib | | pdf | doi | book | abstract]

  3. André Platzer.
    Logical Foundations of Cyber-Physical Systems.
    Springer, Cham, 2018. 659 pages. ISBN 978-3-319-63587-3.
    [bib | | doi | slides | video | book | web | errata | abstract]

  4. Stefan Mitsch, André Platzer, Werner Retschitzegger and Wieland Schwinger.
    Logic-based modeling approaches for qualitative and hybrid reasoning in dynamic spatial systems.
    ACM Computing Surveys 48(1), pp. 3:1-3:40. 2015. © ACM
    [bib | | pdf | doi | abstract]

  5. Jan-David Quesel, Stefan Mitsch, Sarah Loos, Nikos Aréchiga, and André Platzer.
    How to model and prove hybrid systems with KeYmaera: A tutorial on safety.
    STTT 18(1), pp. 67-91, 2016. © The authors
    [bib | | pdf | doi | mypdf | abstract]

  6. André Platzer.
    Analog and hybrid computation: Dynamical systems and programming languages.
    Bulletin of the EATCS 114, 2014. © The author
    Invited paper in The Logic in Computer Science Column by Yuri Gurevich.
    [bib | | pdf | eprint | abstract]

  7. André Platzer.
    Dynamic logics of dynamical systems.
    arXiv:1205.4788, May 2012. Long version of LICS'12 invited tutorial.
    [bib | | pdf | arXiv | LICS'12 | abstract]

  8. André Platzer.
    Logics of dynamical systems.
    ACM/IEEE Symposium on Logic in Computer Science, LICS 2012, June 25–28, 2012, Dubrovnik, Croatia, pp. 13-24. IEEE 2012. © IEEE
    Invited paper.
    [bib | | pdf | doi | slides | abstract]

  9. André Platzer.
    Logic and compositional verification of hybrid systems.
    In Ganesh Gopalakrishnan and Shaz Qadeer, editors, Computer Aided Verification, CAV 2011, Snowbird, UT, USA, Proceedings, volume 6806 of LNCS, pp. 28-43. Springer, 2011. © Springer
    Invited tutorial.
    [bib | | pdf | doi | slides | abstract]

  10. André Platzer.
    Logical Analysis of Hybrid Systems:
       Proving Theorems for Complex Dynamics.
    Springer, Heidelberg, 2010. 426 pages. ISBN 978-3-642-14508-7.
    [bib | | doi | book | web | errata | abstract]

  11. André Platzer.
    Differential Dynamic Logics:
       Automated Theorem Proving for Hybrid Systems.
    PhD Thesis, Department of Computing Science, University of Oldenburg, 2008.
    ACM Doctoral Dissertation Honorable Mention Award in 2009.
    Extended version appeared as book Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics, Springer, 2010.
    [bib | | pdf | eprint | slides | book | ebook | abstract]

High-Level Surveys

A concise but compelling narrative of the high-level goals and approaches is in an invited paper at IJCAR'16 [1].
  1. André Platzer.
    The logical path to autonomous cyber-physical systems.
    In David Parker and Verena Wolf, editors, International Conference on Quantitative Evaluation of SysTems, QEST 2019, Glasgow, UK, Proceedings, volume 11785 of LNCS, pp. 25-33. Springer, 2019. © Springer
    Invited paper.
    [bib | | pdf | doi | slides | abstract]

  2. André Platzer.
    Logic & proofs for cyber-physical systems.
    In Nicola Olivetti and Ashish Tiwari, editors, Automated Reasoning, 8th International Joint Conference, IJCAR 2016, Coimbra, Portugal, Proceedings, volume 9706 of LNCS, pp. 15-21. Springer, 2016. © Springer
    Invited paper.
    [bib | | pdf | doi | slides | abstract]

  3. André Platzer.
    Logical analysis of hybrid systems:
       A complete answer to a complexity challenge.
    Journal of Automata, Languages and Combinatorics 17(2-4), pp. 265-275. 2012.
    Invited Paper
    [bib | | pdf | doi | abstract]

  4. André Platzer.
    Verification of cyberphysical transportation systems.
    IEEE Intelligent Systems 24(4), pp. 10-13, Jul/Aug, 2009. © IEEE
    Invited paper.
    [bib | | doi | abstract]

  5. André Platzer.
    Differential dynamic logic:
       Automated theorem proving for hybrid systems.
    Künstliche Intelligenz 24(1), pp. 75-77, 2010. © Springer
    Invited paper.
    [bib | | doi | abstract]

Other

Arithmetic & Computer Algebra

  1. Katherine Kosaian, Yong Kiam Tan, and André Platzer.
    A first complete algorithm for real quantifier elimination in Isabelle/HOL.
    CPP 2023, Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs, pp. 211-224. ACM, 2023. © ACM
    [bib | | pdf | doi | video | Isabelle | arXiv | abstract]

  2. Matias Scharager, Katherine Cordwell, Stefan Mitsch and André Platzer.
    Verified quadratic virtual substitution for real arithmetic.
    In Marieke Huisman, Corina Pasareanu, and Naijun Zhan, editors, FM 2021: Formal Methods, volume 13047 of LNCS, pp. 200-217. Springer, 2021. © Springer
    [bib | | pdf | doi | slides | Isabelle | arXiv | abstract]

  3. Katherine Cordwell, Yong Kiam Tan and André Platzer.
    A verified decision procedure for univariate real arithmetic with the BKR algorithm.
    In Liron Cohen and Cezary Kaliszyk, editors, 12th International Conference on Interactive Theorem Proving, ITP 2021, June 29-July 1, 2021, Rome, Italy, volume 193 of LIPIcs, pp. 14:1-14:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik 2021. © The authors
    [bib | | pdf | doi | slides | Isabelle | arXiv | abstract]

  4. Sicun Gao, André Platzer and Edmund M. Clarke.
    Quantifier elimination over finite fields with Gröbner bases.
    In Franz Winkler, editor, Algebraic Informatics, Fourth International Conference, CAI 2011, Linz, Austria, June 21-24, 2011, Proceedings, volume 6742 of LNCS, pp. 140-157. Springer, 2011. © Springer
    [bib | | pdf | doi | arXiv | abstract]

  5. André Platzer.
    Logical Analysis of Hybrid Systems:
       Proving Theorems for Complex Dynamics.
    Springer, Heidelberg, 2010. 426 pages. ISBN 978-3-642-14508-7.
    [bib | | doi | book | web | errata | abstract]

  6. André Platzer, Jan-David Quesel and Philipp Rümmer.
    Real world verification.
    In Renate A. Schmidt, editor, International Conference on Automated Deduction, CADE-22, Montreal, Canada, Proceedings, volume 5663 of LNCS, pp. 485-501. Springer, 2009. © Springer
    [bib | | pdf | doi | slides | TR | smtlib | abstract]
    Introduces a decision procedure for universal nonlinear real arithmetic combining Gröbner bases and semidefinite programming for the Real Nullstellensatz.

  7. André Platzer.
    Differential Dynamic Logics:
       Automated Theorem Proving for Hybrid Systems.
    PhD Thesis, Department of Computing Science, University of Oldenburg, 2008.
    ACM Doctoral Dissertation Honorable Mention Award in 2009.
    Extended version appeared as book Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics, Springer, 2010.
    [bib | | pdf | eprint | slides | book | ebook | abstract]

  8. André Platzer.
    Combining deduction and algebraic constraints for hybrid system analysis.
    In Bernhard Beckert, editor, 4th International Verification Workshop, VERIFY'07, Workshop at Conference on Automated Deduction (CADE), Bremen, Germany, CEUR Workshop Proceedings, 259:164-178, 2007.
    [bib | | pdf | eprint | slides | abstract]

Architecture

  1. Akshay Rajhans, Ajinkya Bhave, Ivan Ruchkin, Bruce H. Krogh, David Garlan, André Platzer and Bradley Schmerl.
    Supporting heterogeneity in cyber-physical systems architectures.
    IEEE Transactions on Automatic Control 59(12), pp. 3178-3193, 2014.
    Special issue on Control of Cyber-Physical Systems. © IEEE
    [bib | | pdf | doi | abstract]

  2. Akshay Rajhans, Ajinkya Bhave, Sarah M. Loos, Bruce H. Krogh, André Platzer and David Garlan.
    Using parameters in architectural views to support heterogeneous design and verification.
    In 50th IEEE Conference on Decision and Control and European Control Conference CDC. pp. 2705-2710, IEEE. 2011. © IEEE
    [bib | | pdf | doi | TAC'14 | abstract]

Education

  1. André Platzer.
    Logical Foundations of Cyber-Physical Systems.
    Springer, Cham, 2018. 659 pages. ISBN 978-3-319-63587-3.
    [bib | | doi | slides | video | book | web | errata | abstract]

  2. Sarah M. Loos and André Platzer.
    Teaching Cyber-Physical Systems with Logic.
    Draft, 2014.
    [bib | | pdf | course | abstract]

  3. André Platzer.
    Teaching CPS foundations with contracts.
    First Workshop on Cyber-Physical Systems Education (CPS-Ed 2013), pp. 7-10. 2013.
    [bib | | pdf | eprint | slides | poster | course | abstract]

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