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]