This paper addresses the problem of computing symbolically the set of reachable configurations of a linear hybrid automaton.
A solution proposed in earlier work consists in exploring the reachable configurations using an acceleration operator for computing the iterated effect of selected control cycles. Unfortunately, this method imposes a periodicity requirement
on the data transformations labeling these cycles, that is not always satisfied in practice. This happens in particular with
the important subclass of timed automata, even though it is known that the paths of such automata have a periodic behavior.
The goal of this paper is to broaden substantially the applicability of hybrid acceleration. This is done by introducing powerful
reduction rules, aimed at translating hybrid data transformations into equivalent ones that satisfy the periodicity criterion.
In particular, we show that these rules always succeed in the case of timed automata. This makes it possible to compute an
exact symbolic representation of the set of reachable configurations of a linear hybrid automaton, with a guarantee of termination
over the subclass of timed automata. Compared to other known solutions to this problem, our method is simpler, and applicable
to a much larger class of systems.