Highly fault-tolerant sorting circuits

The problem of constructing a sorting circuit that will work well even if a constant fraction of its comparators fail at random is addressed. Two types of comparator failure are considered: passive failures, which result in no comparison being made (i.e., the items being compared are output in the same order that they are input), and destructive failures, which result in the items being output in the reverse of the correct order. In either scenario, it is assumed that each comparator is faulty with some constant probability ρ, and a circuit is said to be fault-tolerant if it performs some desired function with high probability given that each comparator fails with probability ρ. One passive and two destructive circuits are constructed