The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Global qualitative description of a class of nonlinear dynamical systems
Artificial Intelligence
Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Program analysis as constraint solving
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Invariant synthesis for combined theories
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Approximate reachability for linear systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Generating polynomial invariants for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
Synthesizing Switching Logic Using Constraint Solving
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Proving Termination of Integer Term Rewriting
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Dimensions in program synthesis
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Switching logic synthesis for reachability
EMSOFT '10 Proceedings of the tenth ACM international conference on Embedded software
Generating invariants for non-linear hybrid systems by linear algebraic methods
SAS'10 Proceedings of the 17th international conference on Static analysis
Satisfiability of non-linear (Ir)rational arithmetic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Proceedings of the 14th international conference on Hybrid systems: computation and control
Path-based inductive synthesis for program inversion
Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
Verification and synthesis using real quantifier elimination
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Relational abstractions for continuous and hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Computing semi-algebraic invariants for polynomial dynamical systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Formal verification of hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Differential dynamic logics: automated theorem proving for hybrid systems
Differential dynamic logics: automated theorem proving for hybrid systems
Finite abstractions for hybrid systems with stable continuous dynamics
Discrete Event Dynamic Systems
Hierarchical reasoning for the verification of parametric systems
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Transcendental inductive invariants generation for non-linear differential and hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Algebraic analysis on asymptotic stability of switched hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Verification of Periodically Controlled Hybrid Systems: Application to an Autonomous Vehicle
ACM Transactions on Embedded Computing Systems (TECS) - Special Section on CAPA'09, Special Section on WHS'09, and Special Section VCPSS' 09
Verification of Safety and Liveness Properties of Metric Transition Systems
ACM Transactions on Embedded Computing Systems (TECS) - Special Section on CAPA'09, Special Section on WHS'09, and Special Section VCPSS' 09
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Real algebraic strategies for metitarski proofs
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Timed relational abstractions for sampled data control systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Discovering polynomial Lyapunov functions for continuous dynamical systems
Journal of Symbolic Computation
Hierarchical reasoning and model generation for the verification of parametric hybrid systems
CADE'13 Proceedings of the 24th international conference on Automated Deduction
Exponential-Condition-Based barrier certificate generation for safety verification of hybrid systems
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Automated Reasoning and Mathematics
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
Safety verification for linear systems
Proceedings of the Eleventh ACM International Conference on Embedded Software
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This paper presents a constraint-based technique for discovering a rich class of inductive invariants (boolean combinations of polynomial inequalities of bounded degree) for verification of hybrid systems. The key idea is to introduce a template for the unknown invariants and then translate the verification condition into an 茂戮驴 茂戮驴 constraint, where the template unknowns are existentially quantified and state variables are universally quantified. The verification condition for continuous dynamics encodes that the system does not exit the invariant set from any point on the boundary of the invariant set. The 茂戮驴 茂戮驴 constraint is transformed into 茂戮驴 constraint using Farkas lemma. The 茂戮驴 constraint is solved using a bit-vector decision procedure. We present preliminary experimental results that demonstrate the feasibility of our approach of solving the 茂戮驴 茂戮驴 constraints generated from models of real-world hybrid systems.