Distributed Event Clock Automata

In distributed real-time systems, we cannot assume that clocks are perfectly synchronized. To model them, we borrow independent clocks from independent clocks timed automata (icTA). First, we define the timed universal and existential semantics icTA. The emptiness of universal timed language of an icTA, and the timed language inclusion of icTA are undecidable. To recover decidability, we propose Recursive Distributed Event Clock Automata (DECA). DECA are closed under all boolean operations and their timed language inclusion problem is decidable (more precisely PSPACE-complete), allowing stepwise refinement. We also propose Distributed Event Clock Temporal Logic (DECTL), a realtime logic with independent time evolutions. This logic can be model-checked by translating a DECTL formula into a DECA automaton.