By Rajeev Alur; T A Henzinger; Stanford University. Computer Science Department

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12 [Module properties under variable hiding] Variable hiding preserves the cardinality, closure, and round-sensitivity properties of modules. Hiding preserves determinism, but may not preserve private determinism. By hiding a variable in a synchronous module we may obtain an asynchronous module. 13 [Abstract block diagrams as abstract types] Every block diagram for a module P , no matter how abstract, contains four pieces of information: the read external variables, the awaited external variables, the interface variables, and the derived await dependencies of P .

30 uses many rounds for a single handshake. The two protocols have identical receiver agents. Every send-receive cycle of AsyncMsg consists of four phases —a message production phase, an agent coordination phase, a message transmission phase, and a message consumption phase— each consisting of any number of update rounds. During the message production phase, the sender (pc = produce) takes an unknown number of rounds to produce a message. During the agent coordination phase, the sender (pc = wait ) waits for an external ready event, which signals the readiness of the receiver to receive a message.

Private determinism The module P has private determinism if all private variables in privXP are controlled by deterministic atoms. Otherwise, P has private nondeterminism. 11 [Determinism vs. private determinism vs. 10 are deterministic. The module AsyncSquare is nondeterministic, because it requires an arbitrary number of rounds for processing an input value. However, AsyncSquare has private determinism, because the initial value of the private queue buffer is uniquely determined by the initial values of the observable variables in and out, and in every update round, the next value of buffer is uniquely determined by the current value of buffer and the current and next values of in and out.

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