Nonlinear ordinary differential equations (2nd ed.)
Nonlinear ordinary differential equations (2nd ed.)
SIAM Review
Lower bound functions for polynomials
Journal of Computational and Applied Mathematics
Convex Optimization
Application of Symbolic Approach to the Bernstein Expansion for Program Analysis and Optimization
Programming and Computing Software
Mathematical analysis of programs
Mathematical analysis of programs
Hybridization methods for the analysis of nonlinear systems
Acta Informatica - Hybrid Systems
The image computation problem in hybrid systems model checking
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Symbolic model checking of hybrid systems using template polyhedra
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Approximate reachability computation for polynomial systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Efficient computation of reachable sets of linear time-invariant systems with inputs
HSCC'06 Proceedings of the 9th 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 comparison of methods for the computation of affine lower bound functions for polynomials
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
Automatic abstraction of non-linear systems using change of bases transformations
Proceedings of the 14th international conference on Hybrid systems: computation and control
Relational abstractions for continuous and hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Transcendental inductive invariants generation for non-linear differential and hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Reachability analysis of polynomial systems using linear programming relaxations
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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This paper is concerned with the problem of computing the image of a set by a polynomial function. Such image computations constitute a crucial component in typical tools for set-based analysis of hybrid systems and embedded software with polynomial dynamics, which found applications in various engineering domains. One typical example is the computation of all states reachable from a given set in one step by a continuous dynamics described by a differential or difference equation. We propose a new algorithm for over-approximating such images based on the Bernstein expansion of polynomial functions. The images are stored using template polyhedra. Using a prototype implementation, the performance of the algorithm was demonstrated on two practical systems as well as a number of randomly generated examples.