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Synchronization and fault tolerance of processes are emphasis in the distributed systems research, but only a few people involves in the mathematics model used in processes synchronization and fault tolerance yet. This paper takes distributed system as an event driven system, classify the events that cause system state variety into four classes, and proposed an extended finite state machine (EFSM) with synchronization and fault tolerant message to the distributed system. Accordingly, a checkpoint set up algorithm based in this EFSM is proposed. During the establishing of the checkpoint, the consistency of checkpoint can be determined by calculating the number of sending and receiving messages. In case of lost message, sending and receiving process that lost message can be found by checking the number of sending and receiving messages, and the lost messages can be retransmitted and received. Thus the establishing of the distributed systems global state has been simplified.