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We show that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum two player game problems.
Stochastic games with perfect information and time average payoff
T. M. Liggett and S. A. Lippman · 1969
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A general separation theorem in extremal algebras
K. Zimmermann · 1977
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L’indépendance linéaire dans les dioïdes
M. Gondran and M. Minoux · 1978
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A characterization of the minimum mean-cycle in a digraph
R.M. Karp · 1978
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Positional strategies for mean payoff games
A. Ehrenfeucht and J. Mycielski · 1979
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Invariant half-lines of nonexpansive piecewise-linear transformations
E. Kohlberg · 1980
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Convexity and log convexity for the spectral radius
R. D. Nussbaum · 1986
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Cyclic games and an algorithm to find minimax cycle means in directed graphs
V. A. Gurvich, A. V. Karzanov, and L. G. Khachiyan · 1988
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Linear systems in ( max , + ) (\max,+) -algebra
M. Plus · 1990
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Eigenvalues of dynamic min-max systems
G.J. Olsder · 1991
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The complexity of stochastic games
A. Condon · 1992
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Maximal minors and their leading terms
B. Sturmfels and A. Zelevinsky · 1993
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Strong regularity of matrices — a survey of results
P. Butkovič · 1994
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Min-max functions
J. Gunawardena · 1994
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On the existence of cycle times for some nonexpansive maps
J. Gunawardena and M. Keane · 1995
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The complexity of mean payoff games on graphs
U. Zwick and M. Paterson · 1996
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Competitive Markov decision processes
J. A. Filar and K. Vrieze · 1997
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Methods and applications of (max,+) linear algebra
S. Gaubert and M. Plus · 1997
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Some ergodic results on stochastic iterative discrete events systems
J.M. Vincent · 1997
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The duality theorem for min-max functions
S. Gaubert and J. Gunawardena · 1998
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A non-linear hierarchy for discrete event dynamical systems
S. Gaubert and J. Gunawardena · 1998
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Max-plus algebra and system theory: where we are and where to go now
G. Cohen, S. Gaubert, and J.P. Quadrat · 1999
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A constructive fixed point theorem for min-max functions
J. Cochet-Terrasson, S. Gaubert, and J. Gunawardena · 1999
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Hahn-Banach separation theorem for max-plus semimodules
G. Cohen, S. Gaubert, and J. P. Quadrat · 2001
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Idempotent functional analysis: an algebraic approach
G.L. Litvinov, V.P. Maslov, and G.B. Shpiz · 2001
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An operator approach to zero-sum repeated games
D. Rosenberg and S. Sorin · 2001
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Topical and sub-topical functions, downward sets and abstract convexity
A. M. Rubinov and I. Singer · 2001
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Eigenvalues for a class of homogeneous cone maps arising from max-plus operators
J. Mallet-Paret and R. Nussbaum · 2002
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Extension of order-preserving maps on a cone
A. D. Burbanks, R. D. Nussbaum, and C. T. Sparrow · 2003
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Max-algebra: the linear algebra of combinatorics?
P. Butkovič · 2003
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From max-plus algebra to nonexpansive maps: a nonlinear theory for discrete event systems
J. Gunawardena · 2003
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Stochastic games and nonexpansive maps
A. Neyman · 2003
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Max-plus ( A , B ) (A,B) -invariant spaces and control of timed discrete event systems
R. D. Katz · 2007
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Max-plus convex sets and max-plus semispaces. I
V. Nitica and I. Singer · 2007
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Inferring min and max invariants using max-plus polyhedra
X. Allamigeon, S. Gaubert, and É. Goubault · 2008
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Exponential behaviour of the Butkovic-Zimmermann algorithm for solving two-sided linear systems in max-algebra
M. Bezem, R. Nieuwenhuis, and E. Rodríguez Carbonell · 2008
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The max-atom problem and its relevance
M. Bezem, R. Nieuwenhuis, and E. Rodríguez Carbonell · 2008
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Cyclic projectors and separation theorems in idempotent convex geometry
S. Gaubert and S. Sergeev · 2008
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𝔹 \mathbb{B} -convexity
W. Briec and C. Horvath · 2004
Cited alongside, same era.
Duality and separation theorems in idempotent semimodules
G. Cohen, S. Gaubert, and J. P. Quadrat · 2004
Cited alongside, same era.
Tropical convexity
M. Develin and B. Sturmfels · 2004
Cited alongside, same era.
The Perron-Frobenius theorem for homogeneous, monotone functions
S. Gaubert and J. Gunawardena · 2004
Cited alongside, same era.
Scheduling with AND/OR precedence constraints
R. H. Möhring, M. Skutella, and F. Stork · 2004
Cited alongside, same era.
Max-plus convex sets and functions
G. Cohen, S. Gaubert, J. P. Quadrat, and I. Singer · 2005
Cited alongside, same era.
Later among the works it cites.
The tropical rank of a tropical matrix
Z. Izhakian · 2008
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A deterministic subexponential algorithm for solving parity games
M. Jurdziński, M. Paterson, and U. Zwick · 2008
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Linear independence over tropical semirings and beyond
M. Akian, S. Gaubert, and A. Guterman · 2009
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Mean-payoff games and the max-atom problem
A. Atserias and E. Maneva · 2009
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An exponential lower bound for the parity game strategy improvement algorithm as we know it
O. Friedmann · 2009
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The tropical analogue of polar cones
S. Gaubert and R. D. Katz · 2009
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Supertropical matrix algebra ii: Solving tropical equations
Z. Izhakian and L. Rowen · 2009
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The tropical rank of a tropical matrix
Z. Izhakian and L. Rowen · 2009
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Tropical convex hull computations
M. Joswig · 2009
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From parity and payoff games to linear programming
S. Schewe · 2009
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The correspondence between tropical convexity and mean payoff games
M. Akian, S. Gaubert, and A. Guterman · 2010
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The tropical double description method
X. Allamigeon, S. Gaubert, and É. Goubault · 2010
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The number of extreme points of tropical polyhedra
X. Allamigeon, S. Gaubert, and R. Katz · 2010
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Hard problems in max-algebra, control theory, hypergraphs and other areas
M. Bezem, R. Nieuwenhuis, and E. Rodríguez Carbonell · 2010
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Tropical linear programming and parametric mean payoff games
S. Gaubert, R. D. Katz, and S. Sergeev · 2010
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Carathéodory, Helly and the others in the max-plus world
S. Gaubert and F. Meunier · 2010
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Duality between invariant spaces for max-plus linear discrete event systems
M. Di Loreto, S. Gaubert, R. Katz, and J-J. Loiseau · 2010
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Tropical polar cones, hypergraph transversals, and mean payoff games
X. Allamigeon, S. Gaubert, and R. D. Katz · 2011
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Minimal half-spaces and external representation of tropical polyhedra
S. Gaubert and R. Katz · 2011
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