CIFASIS   20631
CENTRO INTERNACIONAL FRANCO ARGENTINO DE CIENCIAS DE LA INFORMACION Y DE SISTEMAS
Unidad Ejecutora - UE
artículos
Título:
Tropical Fourier-Motzkin Elimination, with an Application to Real-Time Verification
Autor/es:
XAVIER ALLAMIGEON; ULI FAHRENBERG; STÉPHANE GAUBERT; RICARDO D. KATZ; AXEL LEGAY
Revista:
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Editorial:
WORLD SCIENTIFIC PUBL CO PTE LTD
Referencias:
Lugar: London, UK; Año: 2014 vol. 24 p. 569 - 607
ISSN:
0218-1967
Resumen:
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).