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Article Dans Une Revue International Journal of Algebra and Computation Année : 2014

Tropical Fourier–Motzkin elimination, with an application to real-time verification

Résumé

We introduce a generalization of tropical polyhedra able to express both strict and non-strict inequalities. Such inequalities are handled by means of a semiring of germs (encoding infinitesimal perturbations). We develop a tropical analogue of Fourier-Motzkin elimination from which we derive geometrical properties of these polyhedra. In particular, we show that they coincide with the tropically convex union of (non-necessarily closed) cells that are convex both classically and tropically. We also prove that the redundant inequalities produced when performing successive elimination steps can be dynamically deleted by reduction to mean payoff game problems. As a complement, we provide a coarser (polynomial time) deletion procedure which is enough to arrive at a simply exponential bound for the total execution time. These algorithms are illustrated by an application to real-time systems (reachability analysis of timed automata).
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Dates et versions

hal-01087367 , version 1 (26-11-2014)

Identifiants

Citer

Xavier Allamigeon, Axel Legay, Uli Fahrenberg, Ricardo Katz, Stéphane Gaubert. Tropical Fourier–Motzkin elimination, with an application to real-time verification. International Journal of Algebra and Computation, 2014, 24 (5), pp.569 - 607. ⟨10.1142/S0218196714500258⟩. ⟨hal-01087367⟩
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