a) The figure below depicts a system S that is used in a critical mission that...

 

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a) The figure below depicts a system S that is used in a critical mission that lasts for a period of duration T. S is made up of four identical processors, namely C1, C2, C3, and C4, and a voter V. The processors receive identical inputs, operate in parallel on each input and send their results to V. One of the results is selected by V to be sent out as the output of S. C1 C2 C3 C4 S Figure 1: the internal structure of system S. The system is subject to the following five assumptions: i) correct processors produce identical results for a given input; ii) the voter does not fail during the mission period and knows the identity of the sender of a result it receives; iii) at the start of the mission, all processors are correct; during the mission, at most two processors can become permanently faulty; iv) when two processors become faulty, their first failure will not occur for the same input; e.g., if C3 and C4 become faulty during the mission and if C3 has its first failure for the 100th input, C4 either had its first failure for an earlier, say, 90th input or has not failed yet. v) a faulty processor fails only by producing an incorrect result. Assuming that V can match and compare the processors' results for every given input, explain how V can select only the correct result out of the redundant results produced by the processors. Your design must have provisions to handle the case of two faulty processors producing identically incorrect results for a given input; for example, C3 and C4 can have their first failure for 100th and 110th inputs respectively and produce identically incorrect results for the 120th input. a) The figure below depicts a system S that is used in a critical mission that lasts for a period of duration T. S is made up of four identical processors, namely C1, C2, C3, and C4, and a voter V. The processors receive identical inputs, operate in parallel on each input and send their results to V. One of the results is selected by V to be sent out as the output of S. C1 C2 C3 C4 S Figure 1: the internal structure of system S. The system is subject to the following five assumptions: i) correct processors produce identical results for a given input; ii) the voter does not fail during the mission period and knows the identity of the sender of a result it receives; iii) at the start of the mission, all processors are correct; during the mission, at most two processors can become permanently faulty; iv) when two processors become faulty, their first failure will not occur for the same input; e.g., if C3 and C4 become faulty during the mission and if C3 has its first failure for the 100th input, C4 either had its first failure for an earlier, say, 90th input or has not failed yet. v) a faulty processor fails only by producing an incorrect result. Assuming that V can match and compare the processors' results for every given input, explain how V can select only the correct result out of the redundant results produced by the processors. Your design must have provisions to handle the case of two faulty processors producing identically incorrect results for a given input; for example, C3 and C4 can have their first failure for 100th and 110th inputs respectively and produce identically incorrect results for the 120th input.

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