An Overview of Semantics for the Validation of Numerical Programs
- Cite this paper as:
- Martel M. (2005) An Overview of Semantics for the Validation of Numerical Programs. In: Cousot R. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2005. Lecture Notes in Computer Science, vol 3385. Springer, Berlin, Heidelberg
In this article, we introduce a simple formal semantics for floating-point numbers with errors which is expressive enough to be formally compared to the other methods. Next, we define formal semantics for interval, stochastic, automatic differentiation and error series methods. This enables us to formally compare the properties calculated in each semantics to our reference, simple semantics. Most of these methods having been developed to verify numerical intensive codes, we also discuss their adequacy to the formal validation of softwares and to static analysis. Finally, this study is completed by experimental results.
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