Constructing a reliable test&set bit

The problem of computing with faulty shared bits is addressed. The focus is on constructing a reliable test&set bit from a collection of test&set bits of which some may be faulty. Faults are modeled by allowing operations on the faulty bits to return a special distinguished value, signaling that the operation may not have taken place. Such faults are called omission faults. Some of the constructions are required to be gracefully degrading for omission. That is, if the bound on the number of component bits which fail is exceeded, the constructed bit may suffer faults, but only faults which are no more severe than those of the components; and the constructed bit behaves as intended if the number of component bits which fail does not exceed that bound. Several efficient constructions are presented, and bounds on the space required are given. Our constructions for omission faults also apply to other fault models.