Four issues concerning the semantics of Message Flow Graphs

We discuss four issues concerning the semantics of Message Flow Graphs (MFGs). MFGs are extensively used as pictures of message-passing behavior. One type of MFG, Message Sequence Chart (MSC) is ITU Standard Z.120. We require that a system described by an MFG has global states with respect to its message-passing behavior, with transitions between these states effected by atomic message-passing actions. Under this assumption, we argue (a) that the collection of global message states defined by an MFG is finite (whether for synchronous, asynchronous, or partially-asynchronous message-passing); (b) that the unrestricted use of ‘conditions’ requires processes to keep control history variables of potentially unbounded size; (c) that allowing ‘crossing’ messages of the same type implies certain properties of the environment that are neither explicit nor desirable, and (d) that liveness properties of MFGs are more easily expressed by temporal logic formulas over the control states than by Buchi acceptance conditions over the same set of states.