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Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software
TLDR
The IEEE 754 standard, the FLUCTUAT tool, the types of codes to be analyzed and the analysis methodology, together with code examples and analysis results are presented.
Algebraic topology and concurrency
Static Analysis of Numerical Algorithms
TLDR
This work extends a former domain, with an implicitly relational domain for the approximation of the floating-point values of variables, based on affine arithmetic, which allows us to analyze non trivial numerical computations, that no other abstract domain can analyze with such precise results.
Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis
TLDR
A new domain for finding precise numerical invariants of programs by abstract interpretation is introduced, which consists of level sets of non-linear functions and it is shown that the abstract fixpoint equation can be solved accurately by coupling policy iteration and semi-definite programming.
Inferring Min and Max Invariants Using Max-Plus Polyhedra
TLDR
A new numerical abstract domain able to infer min and max invariants over the program variables, based on max-plus polyhedra, is introduced, able to automatically compute precise properties on numerical and memory manipulating programs such as algorithms on strings and arrays.
Static Analyses of the Precision of Floating-Point Operations
TLDR
This article gives a (sketch of a) semantics of its basic operations then abstract them (in the sense of abstract interpretation) to extract information about the possible loss of precision in floating-point operations.
Static Analysis of Finite Precision Computations
We define several abstract semantics for the static analysis of finite precision computations, that bound not only the ranges of values taken by numerical variables of a program, but also the
Components of the Fundamental Category II
TLDR
The fundamental category is studied, a van Kampen theorem is shown to be available on fundamental categories, and a similar theorem for component categories is shown, useful for inductively computing the component category in some circumstances.
Static Analysis by Policy Iteration on Relational Domains
We give a new practical algorithm to compute, in finite time, a fixpoint (and often the least fixpoint) of a system of equations in the abstract numerical domains of zones and templates used for
Static Analysis of the Accuracy in Control Systems: Principles and Experiments
TLDR
A complete survey of a static analysis based on abstract interpretation, and a prototype implementing this analysis for C code, for studying the propagation of rounding errors occurring at every intermediary step in floating-point computations.
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