98 citations · 539 across the 20 of their papers we have counts for
6 papers · 1 filter
Condition numbers of stochastic mean payoff games and what they say about nonarchimedean semidefinite programming
Xavier Allamigeon, Stéphane Gaubert, Ricardo D. Katz +1
Semidefinite programming can be considered over any real closed field, including fields of Puiseux series equipped with their nonarchimedean valuation. Nonarchimedean semidefinite…
Minimal half-spaces and external representation of tropical polyhedra
Stephane Gaubert, Ricardo D. Katz
We give a characterization of the minimal tropical half-spaces containing a given tropical polyhedron, from which we derive a counter example showing that the number of such minima…
Duality between invariant spaces for max-plus linear discrete event systems
Michael Di Loreto, Stephane Gaubert, Ricardo D. Katz +1
We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating bot…
Max-plus (A,B)-invariant spaces and control of timed discrete event systems
Ricardo David Katz
The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. Although this extension pre…
Reachability problems for products of matrices in semirings
Stephane Gaubert, Ricardo Katz
We consider the following matrix reachability problem: given square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix?…
Rational semimodules over the max-plus semiring and geometric approach of discrete event systems
Stephane Gaubert, Ricardo Katz
We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete e…