Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Error Bounds for the Runge-Kutta Single-Step Integration Process
Journal of the ACM (JACM)
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
Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Stochastic Formal Methods: An Application to Accuracy of Numeric Software
HICSS '07 Proceedings of the 40th Annual Hawaii International Conference on System Sciences
GRKLib: a Guaranteed Runge Kutta Library
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
An overview of semantics for the validation of numerical programs
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
A computational model for multi-variable differential calculus
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
HybridFluctuat: A Static Analyzer of Numerical Programs within a Continuous Environment
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Proving the Correctness of the Implementation of a Control-Command Algorithm
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
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We define an abstraction of the continuous variables that serve as inputs to embedded software. In existing static analyzers, these variables are most often abstracted by a constant interval, and this approach has shown its limits. We propose a different method that analyzes in a more precise way the continuous environment. This environment is first expressed as the semantics of a special continuous program, and we define a safe abstract semantics. We introduce the abstract domain of interval valued step functions and show that it safely over-approximates the set of continuous functions. The theory of guaranteed integration is then used to effectively compute an abstract semantics and we prove that this abstract semantics is safe.