E. Asarin, **Equations on Timed Languages.** We continue
investigation of languages, accepted by timed automata of Alur
and Dill. In the paper *E. Asarin, O.
Maler, P. Caspi, A Kleene Theorem for Timed Automata*, in *Proc.
LICS'97** *timed regular expressions equivalent to
timed automata were introduced. Here we introduce quasilinear *equations
over timed languages *with regular coefficients. We prove
that the minimal solution of such an equation is regular and give
an algorithm to calculate this solution. This result is used to
obtain a new proof of our "Kleene" theorem for timed
automata. Equations over timed languages can be also considered
as an alternative way of specifying these languages. [Pdf]