Fault tolerant circuits and probabilistically checkable proofs

We introduce a new model of fault tolerance for Boolean circuits. We consider synchronized circuits and we allow an adversary to choose a small constant fraction of the gates at each level of the circuit to be faulty. We require that even in the presence of such faults the circuit compute a “loose version” of the given function. We show that every symmetric function has a small (size O(n), depth O(log n)) fault tolerant circuit in this model. We also show a perhaps unexpected relation between our model and probabilistically checkable proofs