Abstract interpretation and application to logic programs
Journal of Logic Programming
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Hybridization methods for the analysis of nonlinear systems
Acta Informatica - Hybrid Systems
Computing Differential Invariants of Hybrid Systems as Fixedpoints
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Endomorphisms for Non-trivial Non-linear Loop Invariant Generation
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
Applications of MetiTarski in the Verification of Control and Hybrid Systems
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Morphisms for Non-trivial Non-linear Invariant Generation for Algebraic Hybrid Systems
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Automatic invariant generation for hybrid systems using ideal fixed points
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Generating invariants for non-linear hybrid systems by linear algebraic methods
SAS'10 Proceedings of the 17th international conference on Static analysis
Automatic abstraction of non-linear systems using change of bases transformations
Proceedings of the 14th international conference on Hybrid systems: computation and control
Verification and synthesis using real quantifier elimination
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Generating polynomial invariants for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
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We present the first verification methods that automatically generate bases of invariants expressed by multivariate formal power series and transcendental functions. We discuss the convergence of solutions generated over hybrid systems that exhibit non-linear models augmented with parameters. We reduce the invariant generation problem to linear algebraic matrix systems, from which one can provide effective methods for solving the original problem. We obtain very general sufficient conditions for the existence and the computation of formal power series invariants over multivariate polynomial continuous differential systems. The formal power series invariants generated are often composed by the expansion of some well-known transcendental functions like log or exp and have an analysable closed-form. This facilitates their use to verify safety properties. Moreover, we generate inequality and equality invariants. Our examples, dealing with non-linear continuous evolution similar to those present today in many critical hybrid embedded systems, show the strength of our results and prove that some of them are beyond the limits of other recent approaches.