KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description)

  • André Platzer
  • Jan-David Quesel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5195)


KeYmaera is a hybrid verification tool for hybrid systems that combines deductive, real algebraic, and computer algebraic prover technologies. It is an automated and interactive theorem prover for a natural specification and verification logic for hybrid systems. KeYmaera supports differential dynamic logic, which is a real-valued first-order dynamic logic for hybrid programs, a program notation for hybrid automata. For automating the verification process, KeYmaera implements a generalized free-variable sequent calculus and automatic proof strategies that decompose the hybrid system specification symbolically. To overcome the complexity of real arithmetic, we integrate real quantifier elimination following an iterative background closure strategy. Our tool is particularly suitable for verifying parametric hybrid systems and has been used successfully for verifying collision avoidance in case studies from train control and air traffic management.


dynamic logic automated theorem proving decision procedures computer algebra verification of hybrid systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ábrahám-Mumm, E., Steffen, M., Hannemann, U.: Verification of hybrid systems: Formalization and proof rules in PVS. In: ICECCS, pp. 48–57. IEEE Computer, Los Alamitos (2001)Google Scholar
  2. 2.
    Beckert, B., Hähnle, R., Schmitt, P.H. (eds.): Verification of Object-Oriented Software. LNCS (LNAI), vol. 4334. Springer, Heidelberg (2007)Google Scholar
  3. 3.
    Collins, G.E., Hong, H.: Partial cylindrical algebraic decomposition for quantifier elimination. J. Symb. Comput. 12(3), 299–328 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Davoren, J.M., Nerode, A.: Logics for hybrid systems. IEEE 88(7) (July 2000)Google Scholar
  5. 5.
    Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic logic. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  7. 7.
    Henzinger, T.A.: The theory of hybrid automata. In: LICS, pp. 278–292. IEEE Computer Society, Los Alamitos (1996)Google Scholar
  8. 8.
    Manna, Z., Sipma, H.: Deductive verification of hybrid systems using STeP. In: Henzinger, T.A., Sastry, S.S. (eds.) HSCC 1998. LNCS, vol. 1386. Springer, Heidelberg (1998)Google Scholar
  9. 9.
    Nonnengart, A., Rock, G., Stephan, W.: Using hybrid automata to express realtime properties in VSE-II. In: Russell, I., Kolen, J.F. (eds.) FLAIRS. AAAI Press, Menlo Park (2001)Google Scholar
  10. 10.
    Platzer, A.: Combining deduction and algebraic constraints for hybrid system analysis. In: Beckert, B. (ed.) VERIFY 2007 at CADE 2007, (2007)Google Scholar
  11. 11.
    Platzer, A.: Differential algebraic dynamic logic for differential algebraic programs. (submitted, 2007)Google Scholar
  12. 12.
    Platzer, A.: Differential dynamic logic for verifying parametric hybrid systems. In: Olivetti, N. (ed.) TABLEAUX 2007. LNCS (LNAI), vol. 4548, pp. 216–232. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Platzer, A.: Differential dynamic logic for hybrid systems. J. Autom. Reasoning (to appear, 2008)Google Scholar
  14. 14.
    Platzer, A., Quesel, J.D.: Logical verification and systematic parametric analysis in train control. In: Egerstedt, M., Mishra, B. (eds.) HSCC. LNCS, Springer, Heidelberg (2008)Google Scholar
  15. 15.
    Silva, B.I., Richeson, K., Krogh, B.H., Chutinan, A.: Modeling and verification of hybrid dynamical system using CheckMate. In: ADPM 2000: 4th International Conference on Automation of Mixed Processes: Hybrid Dynamic Systems (2000)Google Scholar
  16. 16.
    Tomlin, C., Pappas, G.J., Sastry, S.: Conflict resolution for air traffic management: a study in multi-agent hybrid systems. IEEE T. Automat. Contr. 43(4) (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • André Platzer
    • 1
  • Jan-David Quesel
    • 1
  1. 1.Department of Computing ScienceUniversity of OldenburgGermany

Personalised recommendations