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

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The module Sync3BitCounter has no derived await dependencies; it is finite, open, nondeterministic (because the initial counter value is arbitrary), privately deterministic, synchronous, and active. 21 shows an initial trajectory of Sync3BitCounter and, for some of the variables, the corresponding timing diagram. 7 {P3} [Synchronous circuits] (a) Define a passive module SyncNor that models a zero-delay Nor gate. 19: One-bit and three-bit binary counters input, and use out for output. (b) Why is hide z in SyncNor [in 1 , in 2 , out := set, z, out] SyncNor [in 1 , in 2 , out := reset, out, z] not a legal definition of a module?

First, the Rml expression x! stands for the assignment x := ¬x, which issues an x event. (If x! ) It follows that the atom that controls x must read x. Second, the Rml expression x? stands for the boolean expression x = x, which checks if an x event is happening. It follows that an atom that does not control x, reads x if and only if it awaits x. Given a module P , we write eventXP for the set of event variables of P . Synchronous communication We are given two agents —a sender and a receiver. The sender produces a message, then sends the message to the receiver and produces another message, etc.

Formal requirements for message-passing protocols will be stated in Chapter ??. 25 has the sender and the receiver synchronize to transmit a message; that is, when ready to send a message, the sender is blocked until the receiver becomes ready to receive, and when ready to receive a message, the receiver is blocked until the sender transmits a message. The synchronization of both agents is achieved by two-way handshaking in three subrounds (or “stages”) within a single update round. The first subround belongs to the atom Stage1 of the receiver.

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A really temporal logic by Rajeev Alur; T A Henzinger; Stanford University. Computer Science Department

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