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Perron–Frobenius theorem for nonnegative multilinear forms and extensions
Performance evaluation of (max, +) automata
- S. Gaubert
- Computer Science, MathematicsIEEE Trans. Autom. Control.
- 1 December 1995
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.
Modeling and analysis of timed Petri nets using heaps of pieces
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.
Duality and separation theorems in idempotent semimodules
Linear independence over tropical semirings and beyond
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.
Numerical Computation of Spectral Elements in Max-Plus Algebra☆
THE DUALITY THEOREM FOR MIN-MAX FUNCTIONS
Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis
- Assalé Adjé, S. Gaubert, É. Goubault
- Computer Science, MathematicsLog. Methods Comput. Sci.
- 20 March 2010
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.
Inferring Min and Max Invariants Using Max-Plus Polyhedra
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.
Tropical Polyhedra are Equivalent to mean Payoff Games
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.