Max-plus algebra in the history of discrete event systems
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[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 …
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 …
concepts, applications, and computational software packages in an easy-to-use handbook …
Tropical polyhedra are equivalent to mean payoff games
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 …
equivalent to zero-sum two player game problems. In particular, we set up an equivalence …
Linear independence over tropical semirings and beyond
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 …
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 …
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 …
measures) on compact Hausdorff spaces defines a functor on the category of compact …
Inferring min and max invariants using max-plus polyhedra
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 …
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 …
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 …
convexity and scaling problems. The latter, which have been studied in nonnegative matrix …