Max-plus algebra in the history of discrete event systems

J Komenda, S Lahaye, JL Boimond… - Annual Reviews in …, 2018 - Elsevier
Max-plus algebra in the history of discrete event systems - ScienceDirect Skip to main
contentSkip to article Elsevier logo Journals & Books Search RegisterSign in View PDF …

[BOG][B] Max-linear systems: theory and algorithms

P Butkovič - 2010 - books.google.com
Recent years have seen a significant rise of interest in max-linear theory and techniques.
Specialised international conferences and seminars or special sessions devoted to max …

[BOG][B] Handbook of linear algebra

L Hogben - 2006 - books.google.com
The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

Tropical polyhedra are equivalent to mean payoff games

M Akian, S Gaubert, A Guterman - International Journal of Algebra …, 2012 - World Scientific
We show that several decision problems originating from max-plus or tropical convexity are
equivalent to zero-sum two player game problems. In particular, we set up an equivalence …

Linear independence over tropical semirings and beyond

M Akian, S Gaubert, A Guterman - Contemporary Mathematics, 2009 - books.google.com
We investigate different notions of linear independence and of matrix rank that are relevant
for max-plus or tropical semirings. The factor rank and tropical rank have already received …

Generators, extremals and bases of max cones

P Butkovič, H Schneider - Linear algebra and its applications, 2007 - Elsevier
Max cones are max-algebraic analogs of convex cones. In the present paper we develop a
theory of generating sets and extremals of max cones in R+ n. This theory is based on the …

Spaces and maps of idempotent measures

MM Zarichnyi - Izvestiya: Mathematics, 2010 - iopscience.iop.org
We prove that the weak* topologization of the set of all idempotent measures (Maslov
measures) on compact Hausdorff spaces defines a functor on the category of compact …

Inferring min and max invariants using max-plus polyhedra

X Allamigeon, S Gaubert, E Goubault - International Static Analysis …, 2008 - Springer
We introduce a new numerical abstract domain able to infer min and max invariants over the
program variables, based on max-plus polyhedra. Our abstraction is more precise than …

Minimal half-spaces and external representation of tropical polyhedra

S Gaubert, RD Katz - Journal of Algebraic Combinatorics, 2011 - Springer
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 …

On visualization scaling, subeigenvectors and Kleene stars in max algebra

H Schneider, P Butkovič - Linear Algebra and its Applications, 2009 - Elsevier
The purpose of this paper is to investigate the interplay arising between max algebra,
convexity and scaling problems. The latter, which have been studied in nonnegative matrix …