Equations on Timed Languages

We continue investigation of languages, accepted by timed automata of Alur and Dill. In [ACM97] 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 Kleene theorem ([ACM97]) for timed automata. Equations over timed languages can be also considered as an alternative way of specifying these languages.

• Type: Conference
• Year: 1998
• Where: HYBRID
• Authors: Eugene Asarin
• Keywords: Control Systems, HYBRID 1998, Regular, Timed Automata, Timed Languages