Computing the Bandwidth of Meager Timed Automata

The bandwidth of timed automata characterizes the quantity of information produced/transmitted per time unit. We previously delimited 3 classes of TA according to the nature of their asymptotic bandwidth: meager, normal, and obese. In this paper, we propose a method, based on a finite-state simply-timed abstraction, to compute the actual value of the bandwidth of meager automata. The states of this abstraction correspond to barycenters of the faces of the simplices in the region automaton. Then the bandwidth is $\log 1\mathrm{/}\mathrm{\mid }{z}_0\mathrm{\mid }$ where $z_0$ is the smallest root (in modulus) of the characteristic polynomial of this finite-state abstraction.