Design and analysis of test schemes for algorithm-based fault tolerance

The design and analysis of test schemes for algorithm-based fault tolerance (ABFT) are examined. The problem is studied under the assumption that no bound is imposed on the size of a test. Upper and lower bounds are established on the number of tests needed to detect a given number of errors. These bounds are sharply different from those previously established under the bounded test size model. The test schemes presented are easy to implement. It is also shown that the design problem for fault detection is NP-hard even when only one fault needs to be detected. It is shown that the analysis problem is, in general, co-NP-complete and hence unlikely to be efficiently solvable. Several restricted versions of the problem that can be solved efficiently are identified. In addition, a new branch-and-bound algorithm for determining the error detectability of a system is presented.<>