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Perron–Frobenius theorem for nonnegative multilinear forms and extensions
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Performance evaluation of (max, +) automata
  • S. Gaubert
  • Computer Science, Mathematics
    IEEE Trans. Autom. Control.
  • 1 December 1995
TLDR
This formalism, which extends both conventional automata and (max,+) linear representations, covers a class of systems with synchronization phenomena and variable schedules and considers performance evaluation in the worst, mean, and optimal cases.
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Modeling and analysis of timed Petri nets using heaps of pieces
TLDR
It is shown that safe timed Petri nets can be represented by special automata over the (max,+) semiring, which compute the height of heaps of pieces, and a heap-based throughput formula is obtained, which is simpler to compute than its traditional timed event graph version.
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Duality and separation theorems in idempotent semimodules
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Linear independence over tropical semirings and beyond
TLDR
The symmetrization of the max-plus algebra is revisited, establishing properties of linear spaces, linear systems, and matrices over the symmetrized max- plus algebra and developing some general technique to prove combinatorial and polynomial identities for matricesover semirings.
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Numerical Computation of Spectral Elements in Max-Plus Algebra☆
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THE DUALITY THEOREM FOR MIN-MAX FUNCTIONS
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Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis
TLDR
A new domain for finding precise numerical invariants of programs by abstract interpretation is introduced, which consists of level sets of non-linear functions and it is shown that the abstract fixpoint equation can be solved accurately by coupling policy iteration and semi-definite programming.
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Inferring Min and Max Invariants Using Max-Plus Polyhedra
TLDR
A new numerical abstract domain able to infer min and max invariants over the program variables, based on max-plus polyhedra, is introduced, able to automatically compute precise properties on numerical and memory manipulating programs such as algorithms on strings and arrays.
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Tropical Polyhedra are Equivalent to mean Payoff Games
TLDR
It is shown that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum two player game problems, and obtained as a corollary a game theoretical proof of the fact that the tropical rank of a matrix coincides with the maximal number of rows (or columns) of the matrix which are linearly independent in the tropical sense.
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