Multi-timed Bisimulation for Distributed Timed Automata

Timed bisimulation is an important technique which can be used for reasoning about behavioral equivalence between different com- ponents of a complex real-time system. The verification of timed bisimu- lation is a difficult and challenging problem because the state explosion caused by both functional and timing constraints must be taken into account. Timed bisimulation was shown decidable for Timed Automata (TA). Distributed TA and TA with Independent Clocks (icTA) were introduced to model Distributed Real-time Systems. They are a variant of TA with local clocks that may not run at the same rate. In this paper, we first propose to extend the theory of Timed Labeled Transition Sys- tems to Multi-Timed Labeled Transition Systems, and relate them by an extension of timed bisimulation to multi-timed bisimulation. We prove the decidability of multi-timed bisimulation and present an EXPTIME algorithm for deciding whether two icTA are multi-timed bisimilar. For multi-timed bisimilarity, an extension of the standard refinement algo- rithm is described.