ARCH-COMP19 Category Report: Hybrid Systems Theorem Proving

This paper reports on the Hybrid Systems Theorem Proving (HSTP) category in the ARCH-COMP Friendly Competition 2019. The most important characteristic features of the HSTP category remain as in the previous edition [MST+18]: i) The flexibility of programming languages as structuring principles for hybrid systems, ii) The unambiguity and precision of program semantics, and iii) The mathematical rigor of logical reasoning principles. The HSTP category especially features many nonlinear and parametric continuous and hybrid systems. Owing to the nature of theorem proving, HSTP again accommodates three modes: A) Automatic in which the entire verification is performed fully automatically without any additional input beyond the original hybrid system and its safety specification. H) Hints in which select proof hints are provided as part of the input problem specification, allowing users to communicate specific advice about the system such as loop invariants. S) Scripted in which a significant part of the verification is done with dedicated proof scripts or problem-specific proof tactics. This threefold split makes it possible to better identify the sources of scalability and efficiency bottlenecks in hybrid systems theorem proving. The existence of all three categories also makes it easier for new tools with a different focus to participate in the competition, wherever they focus on in the spectrum from fast proof checking all the way to full automation. The types of benchmarks considered and experimental findings are described in this paper as well.

[1]  Yiu-Kwong Man,et al.  Computing Closed Form Solutions of First Order ODEs Using the Prelle-Singer Procedure , 1993, J. Symb. Comput..

[2]  Edmund M. Clarke,et al.  Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study , 2009, FM.

[3]  Stefan Ratschan,et al.  Guaranteed Termination in the Verification of Ltl Properties of Non-linear Robust Discrete Time Hybrid Systems , 2005, Int. J. Found. Comput. Sci..

[4]  André Platzer,et al.  Logical Foundations of Cyber-Physical Systems , 2018, Springer International Publishing.

[5]  André Platzer,et al.  Differential Equation Axiomatization: The Impressive Power of Differential Ghosts , 2018, LICS.

[6]  Mieke Massink,et al.  Modelling free flight with collision avoidance , 2001, Proceedings Seventh IEEE International Conference on Engineering of Complex Computer Systems.

[7]  Bin Gu,et al.  Formal Verification of a Descent Guidance Control Program of a Lunar Lander , 2014, FM.

[8]  S. Shankar Sastry,et al.  Conflict resolution for air traffic management: a study in multiagent hybrid systems , 1998, IEEE Trans. Autom. Control..

[9]  E. Voit,et al.  Recasting nonlinear differential equations as S-systems: a canonical nonlinear form , 1987 .

[10]  André Platzer,et al.  CoasterX: A Case Study in Component-Driven Hybrid Systems Proof Automation , 2018, ADHS.

[11]  André Platzer,et al.  KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description) , 2008, IJCAR.

[12]  André Platzer,et al.  European Train Control System: A Case Study in Formal Verification , 2009, ICFEM.

[13]  Zhou Chaochen,et al.  Duration Calculus: A Formal Approach to Real-Time Systems , 2004 .

[14]  Xin Chen,et al.  Lyapunov Function Synthesis Using Handelman Representations , 2013, NOLCOS.

[15]  Martin Fränzle,et al.  Formal Verification of Simulink/Stateflow Diagrams , 2015, ATVA.

[16]  Michel Kieffer,et al.  Construction of parametric barrier functions for dynamical systems using interval analysis , 2015, Autom..

[17]  André Platzer,et al.  ARCH-COMP18 Category Report: Hybrid Systems Theorem Proving , 2018, ARCH@ADHS.

[18]  Shengchao Qin,et al.  Verifying Simulink diagrams via a Hybrid Hoare Logic Prover , 2013, 2013 Proceedings of the International Conference on Embedded Software (EMSOFT).

[19]  André Platzer,et al.  Formal verification of obstacle avoidance and navigation of ground robots , 2016, Int. J. Robotics Res..

[20]  Nathan Fulton,et al.  KeYmaera X: An Axiomatic Tactical Theorem Prover for Hybrid Systems , 2015, CADE.

[21]  Lydia E. Kavraki,et al.  Hybrid systems: from verification to falsification by combining motion planning and discrete search , 2007, CAV.

[22]  Antoine Girard,et al.  Iterative computation of polyhedral invariants sets for polynomial dynamical systems , 2014, 53rd IEEE Conference on Decision and Control.

[23]  Edmund M. Clarke,et al.  Computing differential invariants of hybrid systems as fixedpoints , 2008, Formal Methods Syst. Des..

[24]  André Platzer,et al.  Formally verified differential dynamic logic , 2017, CPP.

[25]  André Platzer,et al.  How to model and prove hybrid systems with KeYmaera: a tutorial on safety , 2015, International Journal on Software Tools for Technology Transfer.

[26]  Naijun Zhan,et al.  Formal Verification of Simulink/Stateflow Diagrams, A Deductive Approach , 2016 .

[27]  André Platzer,et al.  Differential Dynamic Logic for Hybrid Systems , 2008, Journal of Automated Reasoning.

[28]  Liang Zou,et al.  An Improved HHL Prover: An Interactive Theorem Prover for Hybrid Systems , 2015, ICFEM.

[29]  André Platzer,et al.  A Complete Uniform Substitution Calculus for Differential Dynamic Logic , 2016, Journal of Automated Reasoning.

[30]  Ali Jadbabaie,et al.  Safety Verification of Hybrid Systems Using Barrier Certificates , 2004, HSCC.

[31]  George J. Pappas,et al.  A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates , 2007, IEEE Transactions on Automatic Control.

[32]  Tao Tang,et al.  Verifying Chinese Train Control System under a Combined Scenario by Theorem Proving , 2013, VSTTE.

[33]  Jaume Llibre,et al.  Qualitative Theory of Planar Differential Systems , 2006 .

[34]  Chaochen Zhou,et al.  A Calculus for Hybrid CSP , 2010, APLAS.

[35]  Taylor T. Johnson,et al.  Non-linear Continuous Systems for Safety Verification (Benchmark Proposal) , 2016 .

[36]  André Platzer,et al.  Logical Analysis of Hybrid Systems - Proving Theorems for Complex Dynamics , 2010 .

[37]  Lawrence Charles Paulson,et al.  Isabelle/HOL: A Proof Assistant for Higher-Order Logic , 2002 .

[38]  Naijun Zhan,et al.  Computing semi-algebraic invariants for polynomial dynamical systems , 2011, 2011 Proceedings of the Ninth ACM International Conference on Embedded Software (EMSOFT).

[39]  André Platzer,et al.  Logics of Dynamical Systems , 2012, 2012 27th Annual IEEE Symposium on Logic in Computer Science.

[40]  André Platzer,et al.  The Structure of Differential Invariants and Differential Cut Elimination , 2011, Log. Methods Comput. Sci..

[41]  André Platzer,et al.  A Method for Invariant Generation for Polynomial Continuous Systems , 2016, VMCAI.

[42]  Anders P. Ravn,et al.  A Formal Description of Hybrid Systems , 1996, Hybrid Systems.

[43]  He Jifeng,et al.  From CSP to hybrid systems , 1994 .

[44]  André Platzer,et al.  Differential-algebraic Dynamic Logic for Differential-algebraic Programs , 2010, J. Log. Comput..

[45]  John Lygeros,et al.  Hybrid Control Models of Next Generarion AIr Traffic Management , 1996, Hybrid Systems.

[46]  Nathan Fulton,et al.  Bellerophon: Tactical Theorem Proving for Hybrid Systems , 2017, ITP.

[47]  Thomas A. Henzinger,et al.  Beyond HYTECH: Hybrid Systems Analysis Using Interval Numerical Methods , 2000, HSCC.

[48]  Hardi Hungar,et al.  On the Verification of Cooperating Traffic Agents , 2003, FMCO.

[49]  Liyun Dai,et al.  Barrier certificates revisited , 2013, J. Symb. Comput..