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The Zonotope Abstract Domain Taylor1+ [chapter]

Khalil Ghorbal, Eric Goubault, Sylvie Putot
2009 Lecture Notes in Computer Science  
Geometrically, the representation of the abstract values (the joint range of all variables) in our domain is a center-symmetric polytope called zonotope.  ...  For the time being, intervals, convex polyhedra, octagons, and congruences abstract domains are interfaced. We enrich here the library with a domain based on affine forms, called Taylor1+.  ... 
doi:10.1007/978-3-642-02658-4_47 fatcat:4ucmn7na2nd3dkxzfe3wkwtpji

An Accurate Join for Zonotopes, Preserving Affine Input/Output Relations

Eric Goubault, Tristan Le Gall, Sylvie Putot
2012 Electronical Notes in Theoretical Computer Science  
Zonotopes are a convenient abstract domain for the precise analysis of programs with numerical variables.  ...  We end up by showing some experiments conducted on the constrained Taylor1+ domain of Apron.  ...  Experiments The APRON [17] library implements different abstract domains, including the affine sets (Taylor1+ domain). We implemented this new join operator in the Taylor1+ abstract domain.  ... 
doi:10.1016/j.entcs.2012.09.007 fatcat:4gkcpuiaajhvbnszdupoil5j7e

A zonotopic framework for functional abstractions [article]

Eric Goubault, Sylvie Putot
2009 arXiv   pre-print
This article formalizes an abstraction of input/output relations, based on parameterized zonotopes, which we call affine sets.  ...  We describe the abstract transfer functions and prove their correctness, which allows the generation of accurate numerical invariants.  ...  A preliminary version of this domain, dedicated to the analysis of computations in real numbers, is also implemented as an abstract domain -Taylor1+ [8] -of the open-source library APRON [17] .  ... 
arXiv:0910.1763v1 fatcat:pinbqzuasrdlrjmnpj2lh4i4fq

Inner approximated reachability analysis

Eric Goubault, Olivier Mullier, Sylvie Putot, Michel Kieffer
2014 Proceedings of the 17th international conference on Hybrid systems: computation and control - HSCC '14  
Computing a tight inner approximation of the range of a function over some set is notoriously difficult, way beyond obtaining outer approximations.  ...  An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems.  ...  Michel Kieffer is partly supported by the Institut Universitaire de France, 75005 Paris.  ... 
doi:10.1145/2562059.2562113 dblp:conf/hybrid/GoubaultMPK14 fatcat:z4w6m5hx3vhmjpexemevknjhf4