An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems

This paper presents a bounded model checking tool called $${\texttt{Hydlogic}}$$ for hybrid systems. It translates a reachability problem of a nonlinear hybrid system into a predicate logic formula involving arithmetic constraints and checks the satisfiability of the formula based on a satisfiability modulo theories method. We tightly integrate (i) an incremental SAT solver to enumerate the possible sets of constraints and (ii) an interval-based solver for hybrid constraint systems (HCSs) to solve the constraints described in the formulas. The HCS solver verifies the occurrence of a discrete change by using a set of boxes to enclose continuous states that may cause the discrete change. We utilize the existence property of a unique solution in the boxes computed by the HCS solver as (i) a proof of the reachability of a model and (ii) a guide in the over-approximation refinement procedure. Our $${\texttt{Hydlogic}}$$ implementation successfully handled several examples including those with nonlinear constraints.

[1]  T. Henzinger,et al.  Algorithmic Analysis of Nonlinear Hybrid Systems , 1998, CAV.

[2]  Nacim Meslem,et al.  A Hybrid Bounding Method for Computing an Over-Approximation for the Reachable Set of Uncertain Nonlinear Systems , 2009, IEEE Transactions on Automatic Control.

[3]  Jianhua Zhao,et al.  Path-Oriented Reachability Verification of a Class of Nonlinear Hybrid Automata Using Convex Programming , 2010, VMCAI.

[4]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

[5]  Marco Roveri,et al.  Computing Predicate Abstractions by Integrating BDDs and SMT Solvers , 2007, Formal Methods in Computer Aided Design (FMCAD'07).

[6]  Edward A. Lee.  Cyber Physical Systems: Design Challenges , 2008, 2008 11th IEEE International Symposium on Object and Component-Oriented Real-Time Distributed Computing (ISORC).

[7]  Lui Sha,et al.  Cyber-Physical Systems: A New Frontier , 2008, 2008 IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing (sutc 2008).

[8]  Cesare Tinelli,et al.  DPLL( T): Fast Decision Procedures , 2004, CAV.

[9]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[10]  R. Baker Kearfott,et al.  Introduction to Interval Analysis , 2009 .

[11]  Ansgar Fehnker,et al.  Benchmarks for Hybrid Systems Verification , 2004, HSCC.

[12]  Sumit Gulwani,et al.  Constraint-Based Approach for Analysis of Hybrid Systems , 2008, CAV.

[13]  Oded Maler,et al.  Accurate hybridization of nonlinear systems , 2010, HSCC '10.

[14]  Martin Fränzle,et al.  SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems , 2008, ATVA.

[15]  Olaf Stursberg,et al.  Verification of Hybrid Systems Based on Counterexample-Guided Abstraction Refinement , 2003, TACAS.

[16]  Kazunori Ueda,et al.  Interval-based Solving of Hybrid Constraint Systems , 2009, ADHS.

[17]  Martin Fränzle,et al.  Efficient Solving of Large Non-linear Arithmetic Constraint Systems with Complex Boolean Structure , 2007, J. Satisf. Boolean Model. Comput..

[18]  Harald Ruess,et al.  Lazy Theorem Proving for Bounded Model Checking over Infinite Domains , 2002, CADE.

[19]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[20]  Stefan Kowalewski,et al.  An Evaluation of two Recent Reachability Analysis Tools for Hybrid Systems , 2006, ADHS.

[21]  W. Marsden.  I and J , 2012 .

[22]  Marco Bozzano,et al.  Verifying Industrial Hybrid Systems with MathSAT , 2005, BMC@CAV.

[23]  Sriram Sankaranarayanan,et al.  Symbolic Model Checking of Hybrid Systems Using Template Polyhedra , 2008, TACAS.

[24]  Goran Frehse.  PHAVer: Algorithmic Verification of Hybrid Systems Past HyTech , 2005, HSCC.

[25]  Timothy J. Hickey,et al.  Rigorous Modeling of Hybrid Systems Using Interval Arithmetic Constraints , 2004, HSCC.

[26]  Alexandre Goldsztejn,et al.  The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems , 2008, Electron. Notes Theor. Comput. Sci..

[27]  Stefan Ratschan,et al.  Safety Verification of Hybrid Systems by Constraint Propagation Based Abstraction Refinement , 2005, HSCC.

[28]  Philip S. Yu,et al.  Machine Learning in Cyber Trust: Security, Privacy, and Reliability , 2009 .