Some introductive texts on max-plus algebra and Discrete Event Dynamic Systems
- Methods and Applications of (max,+) Linear Algebra, S. Gaubert and M. Plus. Appears in
the Proceedings of
the 14th Annual Symposium on Theoretical Aspects of Computer Science Lubeck, Germany February 27 - March 1, 1997 (STACS'97), pp 261-282,
LNCS 1200, Springer, 1997,
A survey paper with emphasis on linear algebra.
- Two lectures on max-plus algebra, S. Gaubert,
Proceedings of the 26th Spring School of Theoretical Computer Science,
Algèbres Max-Plus et applications en informatique et automatique", Ile de Noirmoutier, 4-7 mai, pages 83--147, 1998. Publisher INRIA,
Le Chesnay, France. These lectures notes contained an original chapter
(Chapter 2) written specially for the school,
dealing with ``Exotic Semirings: Examples and General Results''.
- Max-plus algebra and System Theory: where we are and where to go now.
G. Cohen, S. Gaubert and J.P. Quadrat,
Annual Reviews in Control, vol. 23, pp 207--219, 1999.
M. Akian, R. Bapat, and S. Gaubert.
In L. Hogben, editor, Handbook of Linear Algebra (Discrete
Mathematics and Its Applications), volume 39. Chapman & Hall/CRC, 2006. Chapter 25.
- G. Cohen, S. Gaubert, and J.P. Quadrat
L'algèbre des sandwichs, Pour la Science, pp. 56--63, Février 2005.
Some Lecture Notes
(Postscript, 120p, in French) on max-plus algebras an discrete event systems,
- Max-Plus Algebra and Applications to System Theory and Optimal
Max-Plus Working Group, presented by J.P. Quadrat.
Proceedings of the ICM
Zurich, August 1994.
A shorter survey paper, covering also briefly Bellman processes.
The max-plus approach to Discrete Event Systems, in
a few words (in French)
- Slides - Max-plus algebra: a guided tour, talk at the SIAM Conference on Control and its Applications 09 , S. Gaubert.
- Slides of a talk on max-plus or tropical polyhedra (Montreal Workshop on Tropical Mathematics, July 2009), S. Gaubert
- Slides of the talk on "Tropical modules, zero-sum games and
non-archimedean optimization" (Noncommutative geometry, NCG 2017: number theory, A celebration of Alain Connes' 70th birthday, Shanghai, April 2017),
See also the maxplus.org site.
S. Gaubert Updated Jul. 2009