Definition. The relation on the set of events of a system is the smallest relation satisfying the following three conditions: (1) If and are events in the same process, and comes before , then . (2) If is the sending of a message by one process and is the receipt of the same message by another process, then . (3) If and then . Two distinct events and are said to be concurrent if and .
We assume that for any event a. is an irreflexive partial ordering.
Clock Condition For any events a, b：if a b, then .
C1. If and are events in process and comes before , then .
C2. If is the sending of a message by process and is the receipt of that message by process , then .
IR1. Each process increments between any two successive events.
IR2. (a) If event is the sending of a message m by process , then the message m contains a timestamp . (b) Upon receiving a message m, process sets greater than or equal to its present value and greater than .