Information Sciences: an International Journal
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Temporal verification of reactive systems: safety
Temporal verification of reactive systems: safety
UPPAAL—a tool suite for automatic verification of real-time systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Term rewriting and all that
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
A Technique for Invariant Generation
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
HYTECH: The Cornell HYbrid TECHnology Tool
Hybrid Systems II
Polynomial Constants Are Decidable
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
A Transformational Approach for Generating Non-linear Invariants
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
Algorithmic Analysis of Nonlinear Hybrid Systems
Proceedings of the 7th International Conference on Computer Aided Verification
The d/dt Tool for Verification of Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Approximate reachability for linear systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Computing Differential Invariants of Hybrid Systems as Fixedpoints
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Invariants for Parameterised Boolean Equation Systems
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Invariants for Parameterised Boolean Equation Systems
Theoretical Computer Science
Automatic abstraction of non-linear systems using change of bases transformations
Proceedings of the 14th international conference on Hybrid systems: computation and control
Formal verification of hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
SAT Modulo Linear Arithmetic for Solving Polynomial Constraints
Journal of Automated Reasoning
Model checking of hybrid systems: from reachability towards stability
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Fixed point iteration for computing the time elapse operator
HSCC'06 Proceedings of the 9th 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
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Exercises in nonstandard static analysis of hybrid systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Complementary methodologies for developing hybrid systems with event-b
ICFEM'12 Proceedings of the 14th international conference on Formal Engineering Methods: formal methods and software engineering
Hyperstream processing systems: nonstandard modeling of continuous-time signals
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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We present a new method for generating algebraic invariants of hybrid systems. The method reduces the invariant generation problem to a constraint solving problem using techniques from the theory of ideals over polynomial rings. Starting with a template invariant--a polynomial equality over the system variables with unknown coefficients--constraints are generated on the coefficients guaranteeing that the solutions are inductive invariants. To control the complexity of the constraint solving, several stronger conditions that imply inductiveness are proposed, thus allowing a trade-off between the complexity of the invariant generation process and the strength of the resulting invariants.