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

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Since the two atoms of Pete are speedindependent processes, in any given update round, either none, one, the other, or both atoms may sleep. 24 indicates for every update round which processes proceed. 9 {T3} [Accessibility for Peterson’s protocol] Prove that the module Pete meets the accessibilty requirement. 10 {P3} [Three-process mutual exclusion] You are asked to generalize Peterson’s protocol to the case of three processes: first specify the threeprocess mutual-exclusion problem; then present your solution in the form of a finite module which is a speed-independent three-process set.

Since the program counters pc 1 and pc 2 are interface variables, in every update round, each process “knows” about the current status of the other process. Our task is to add guarded assignments that permit each process to enter its critical section, by updating pc 1 or pc 2 from reqC to inC , in a controlled fashion. We say that the i-th process has the opportunity to enter the critical section if the guard is true for some guarded command that sets pc i to inC . ) In a correct solution to the mutual-exclusion problem, the parallel composition of both processes has to meet several requirements.

The receiver, concurrently, waits to receive a message, then consumes the message and waits to receive another message, etc. We model each agent as a module that cannot observe the control variables of the other agent. The private variable pc of the sender indicates if the agent is producing a message (pc = produce) or attempting to send a message (pc = send ). The sender starts by producing a message: init [] true → pc := produce Messages are produced by the lazy atom Producer , which requires an unknown number of rounds to produce a message.

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

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