The partition method for the order-insensitivity in a synchronous distributed system

Synchronous systems can be distributed using different schemes of distribution. One possible distribution scheme is transforming the synchronous systems into a globally asynchronous locally synchronous system in which each site behaves synchronously while the exchanges between sites are asynchronous; this is a case of synchronous distributed systems. However, the obtained synchronous distributed system will present some bad behaviors due to delays introduced by the partial asynchronous behavior. Thus, we introduce order-insensitivity by analogy with delay-insensitivity of asynchronous hardware in order to have the same behavior in distributed and centralized implementations. This property characterizes systems where the parallel execution is equivalent to all possible sequential executions. Moreover, this property is not an intrinsic property to the state machine but only of its implementation. Consequently, we propose an algorithm for transforming an order-sensitive transition function into an equivalent order-insensitive one