it becomes of great importance in detect test sets which are intended for increased non-targeted fault and defect coverage. Coincidental fault detection A Tutorial on the Flexible Optical Networking Paradigm: State of the Art, Trends, and Research Challenges by randomly fixing some test bits occurs similarly in -detect test sets as in detect test sets. Column of Table I gives of the fully specified detect test set of which is much higher than the targeted detection coverage. This shows a lot of room for relaxation in the -detect test sets. A Tutorial on the Flexible Optical Networking Paradigm: State of the Art, Trends, and Research Challenges At the same time, since the detections were achieved coincidentally, a relaxed test which maintains the -detection fault coverage will recover the reduction in when it will be finally fully specified before test application. Thus, relaxed –detect test sets are expected to maintain their non-targeted fault and defect coverages. A Tutorial on the Flexible Optical Networking Paradigm: State of the Art, Trends, and Research Challenges PROBLEM FORMULATION AND NOTATION Consider a given A Tutorial on the Flexible Optical Networking Paradigm: State of the Art, Trends, and Research Challenges -detect test set for a combinational or a fully-scanned sequential circuit-under-test . A Tutorial on the Flexible Optical Networking Paradigm: State of the Art, Trends, and Research Challenges Each of the test patterns consists of strings of three-valued bits . Consider also a fault model , based on which the list of faults detected by , denoted by , is derived. For the considered fault list, the test set has – A Tutorial on the Flexible Optical Networking Paradigm: State of the Art, Trends, and Research Challenges detect fault coverage, denoted by and specified bits ratio, denoted by , as defined below. The -detect fault coverage of a test set , denotby is the percentage of the faults considered, under a given fault model with fault list that are detected by with at least different tests. Note, that for some faults only different tests exist can be generated by any test generation process. A Tutorial on the Flexible Optical Networking Paradigm: State of the Art, Trends, and Research Challenges Let denote the fault list of all faults in that are detected at least times in . Similarly, let denote the faults in that are detected less than times in . Clearly, . In the case where no tests exist for a fault , then fault is considered to be redundant. In this work, is calculated considering all faults in . Definition For a test set , the ratio of the bits having a specified value A Tutorial on the Flexible Optical Networking Paradigm: State of the Art, Trends, and Research Challenges over the total number of test set bits is defined as the specified bits ratio, denoted by . This ratio gives a test set property that indicates how flexible a test set is. Clearly for any test set The closer the more flexible is. For fully specified test sets, The test set relaxation process refers to replacing test set with a test set such that each of the following constraints is satisfied The above constraints give the specifications of the test set relaxation problem considered. Constraint preserves the –detect fault coverage in the same way as the fault coverage is preserved in single detect test sets. If a fault is detected times in test set then fault is also detected times in the relaxed test set .