21 citations · 29 across the 8 of their papers we have counts for
10 papers
Bounding Fixed Points of Set-Based Bellman Operator and Nash Equilibria of Stochastic Games
Sarah H. Q. Li, Assalé, Adjé +2
Motivated by uncertain parameters encountered in Markov decision processes (MDPs) and stochastic games, we study the effect of parameter uncertainty on Bellman operator-based algor…
Quadratic Maximization of Reachable Values of Stable Discrete-Time Affine Systems
Assalé Adjé
In this paper, we solve a maximization problem where the objective function is quadratic and the constraints set is the reachable values set of a stable discrete-time affine system…
Overapproximating the Reachable Values Set of Piecewise Affine Systems Coupling Policy Iterations with Piecewise Quadratic Lyapunov Functions
Assalé Adjé
We have recently constructed a piecewise quadratic Lyapunov function to prove the boundedness of the reachable values set of piecewise affine discrete-time systems. The method deve…
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…
Quadratic Zonotopes:An extension of Zonotopes to Quadratic Arithmetics
Assalé Adjé, Pierre-Loïc Garoche, Alexis Werey
Affine forms are a common way to represent convex sets of using a base of error terms . Quadratic forms are an extension of affine forms enabling the u…
Polynomial Template Generation using Sum-of-Squares Programming
Assalé Adjé, Victor Magron
Template abstract domains allow to express more interesting properties than classical abstract domains. However, template generation is a challenging problem when one uses template…
Automatic Synthesis of Piecewise Linear Quadratic Invariants for Programs
Assalé Adje, Pierre-Loïc Garoche
Among the various critical systems that worth to be formally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop i…
Concrete Semantics of Programs with Non-Deterministic and Random Inputs
Assalé Adjé, Jean Goubault-Larrecq
This document gives semantics to programs written in a C-like programming language, featuring interactions with an external environment with noisy and imprecise data.
Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis
Assalé Adjé, Stéphane Gaubert, Eric Goubault
We introduce a new domain for finding precise numerical invariants of programs by abstract interpretation. This domain, which consists of level sets of non-linear functions, genera…