84 citations · 342 across the 90 of their papers we have counts for
5 papers · 1 filter
Semidefinite approximations of projections and polynomial images of semialgebraic sets
Victor Magron, Didier Henrion, Jean-Bernard Lasserre
Given a compact semialgebraic set S of R^n and a polynomial map f from R^n to R^m, we consider the problem of approximating the image set F = f(S) in R^m. This includes in particul…
Certified Roundoff Error Bounds Using Semidefinite Programming
Victor Magron, George Constantinides, Alastair Donaldson
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a…
Property-based Polynomial Invariant Generation using Sums-of-Squares Optimization
Assalé Adjé, Pierre-Loïc Garoche, Victor Magron
While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachab…
A Sums-of-Squares Extension of Policy Iterations
Assalé Adjé, Pierre-Loïc Garoche, Victor Magron
In order to address the imprecision often introduced by widening operators in static analysis, policy iteration based on min-computations amounts to considering the characterizatio…
A formal proof of the Kepler conjecture
Thomas Hales, Mark Adams, Gertrud Bauer +19
This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the…