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A hypothetical distributed system uses the Interactive Consistency algorithm (ICA) to achieve Byzantine Agreement. In terms of the TPH-3, there are two fault-scenarios of particular concern: - $a=1,s=2,b=0$, - $a=2,s=0,b=0$. Determine the smallest number of processors $N$ for which there exists a single ICA protocol which can cover both scenarios.

To determine the smallest number of processors (N) for which a single Interactive Consistency Algorithm (ICA) protocol can cover both fault scenarios, let's analyze each scenario individually.

Scenario 1: a=1, s=2, b=0

In this scenario, we have three processors: a, s, and b. The processor labels indicate the number of correct processors (a and b) and the number of faulty processors (s).

For the ICA protocol to achieve Byzantine Agreement in this scenario, it needs to satisfy the conditions:

The number of faulty processors (s) should be less than one-third of the total number of processors (N). s < N/3