Layered Composition for Timed Automata

We investigate layered composition for real-time systems modelled as (networks of) timed automata (TA). We first formulate the principles of layering and transition independence for TA, and demonstrate the validity of the communication closed layer (CCL) laws in such a setting, by means of an operator for layered composition that is intermediate between parallel and sequential composition. Next, we introduce the principles of input/output (i/o) and partial-order (po) equivalences, and show that such equivalences are preserved when the layered composition operator is replaced by sequential composition within the expressions appearing in the CCL laws. Finally, we proceed to show that such layering (together with equivalences obtained through the CCL laws) can be useful in the design and verification of dense real-time systems that consist of a network of interacting components, by bringing about a reduction of the state-space through the exploitation of transition independence. This is illustrated by considering a collision avoidance protocol developed for an audio/video system of Bang and Olufsen.