The modern electronic testing has a forty year history. Test professionals hold some fairly large conferences and numerous workshops, have a journal, and there are over one hundred books on testing. Still, a full course on testing is offered only at a few universities, mostly by professors who have a research interest in this area. Apparently, most professors would not have taken a course on electronic testing when they were students. Other than the computer engineering curriculum being too crowded, the major reason cited for the absence of a course on electronic testing is the lack of a suitable textbook. For VLSI the foundation was provided by semiconductor device techn- ogy, circuit design, and electronic testing. In a computer engineering curriculum, therefore, it is necessary that foundations should be taught before applications. The field of VLSI has expanded to systems-on-a-chip, which include digital, memory, and mixed-signalsubsystems. To our knowledge this is the first textbook to cover all three types of electronic circuits. We have written this textbook for an undergraduate "foundations" course on electronic testing. Obviously, it is too voluminous for a one-semester course and a teacher will have to select from the topics. We did not restrict such freedom because the selection may depend upon the individual expertise and interests. Besides, there is merit in having a larger book that will retain its usefulness for the owner even after the completion of the course. With equal tenacity, we address the needs of three other groups of readers.

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 9 QUADRATIC 0-1 PROGRAMMING 8S 9. 1 Energy Minimization 86 9. 2 Notation and Tenninology . . . . . . . . . . . . . . . . . 87 9. 3 Minimization Technique . . . . . . . . . . . . . . . . . . 88 9. 4 An Example . . . . . . . . . . . . . . . . . . . . . . . . 92 9. 5 Accelerated Energy Minimization. . . . . . . . . . . . . 94 9. 5. 1 Transitive Oosure . . . . . . . . . . . . . . . . . 94 9. 5. 2 Additional Pairwise Relationships 96 9. 5. 3 Path Sensitization . . . . . . . . . . . . . . . . . 97 9. 6 Experimental Results 98 9. 7 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . 100 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 10 TRANSITIVE CLOSURE AND TESTING 103 10. 1 Background . . . . . . . . . . . . . . . . . . . . . . . . 104 10. 2 Transitive Oosure Definition 105 10. 3 Implication Graphs 106 10. 4 A Test Generation Algorithm 107 10. 5 Identifying Necessary Assignments 112 10. 5. 1 Implicit Implication and Justification 113 10. 5. 2 Transitive Oosure Does More Than Implication and Justification 115 10. 5. 3 Implicit Sensitization of Dominators 116 10. 5. 4 Redundancy Identification 117 10. 6 Summary 119 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 11 POLYNOMIAL-TIME TESTABILITY 123 11. 1 Background 124 11. 1. 1 Fujiwara's Result 125 11. 1. 2 Contribution of the Present Work . . . . . . . . . 126 11. 2 Notation and Tenninology 127 11. 3 A Polynomial TlDle Algorithm 128 11. 3. 1 Primary Output Fault 129 11. 3. 2 Arbitrary Single Fault 135 11. 3. 3 Multiple Faults. . . . . . . . . . . . . . . . . . . 137 11. 4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . 139 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 ix 12 SPECIAL CASES OF HARD PROBLEMS 141 12. 1 Problem Statement 142 12. 2 Logic Simulation 143 12. 3 Logic Circuit Modeling . 146 12. 3. 1 Modelfor a Boolean Gate . . . . . . . . . . . . . 147 12. 3. 2 Circuit Modeling 148 12.

The modern electronic testing has a forty year history. Test professionals hold some fairly large conferences and numerous workshops, have a journal, and there are over one hundred books on testing. Still, a full course on testing is offered only at a few universities, mostly by professors who have a research interest in this area. Apparently, most professors would not have taken a course on electronic testing when they were students. Other than the computer engineering curriculum being too crowded, the major reason cited for the absence of a course on electronic testing is the lack of a suitable textbook. For VLSI the foundation was provided by semiconductor device techn- ogy, circuit design, and electronic testing. In a computer engineering curriculum, therefore, it is necessary that foundations should be taught before applications. The field of VLSI has expanded to systems-on-a-chip, which include digital, memory, and mixed-signalsubsystems. To our knowledge this is the first textbook to cover all three types of electronic circuits. We have written this textbook for an undergraduate "foundations" course on electronic testing. Obviously, it is too voluminous for a one-semester course and a teacher will have to select from the topics. We did not restrict such freedom because the selection may depend upon the individual expertise and interests. Besides, there is merit in having a larger book that will retain its usefulness for the owner even after the completion of the course. With equal tenacity, we address the needs of three other groups of readers.

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 9 QUADRATIC 0-1 PROGRAMMING 8S 9. 1 Energy Minimization 86 9. 2 Notation and Tenninology . . . . . . . . . . . . . . . . . 87 9. 3 Minimization Technique . . . . . . . . . . . . . . . . . . 88 9. 4 An Example . . . . . . . . . . . . . . . . . . . . . . . . 92 9. 5 Accelerated Energy Minimization. . . . . . . . . . . . . 94 9. 5. 1 Transitive Oosure . . . . . . . . . . . . . . . . . 94 9. 5. 2 Additional Pairwise Relationships 96 9. 5. 3 Path Sensitization . . . . . . . . . . . . . . . . . 97 9. 6 Experimental Results 98 9. 7 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . 100 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 10 TRANSITIVE CLOSURE AND TESTING 103 10. 1 Background . . . . . . . . . . . . . . . . . . . . . . . . 104 10. 2 Transitive Oosure Definition 105 10. 3 Implication Graphs 106 10. 4 A Test Generation Algorithm 107 10. 5 Identifying Necessary Assignments 112 10. 5. 1 Implicit Implication and Justification 113 10. 5. 2 Transitive Oosure Does More Than Implication and Justification 115 10. 5. 3 Implicit Sensitization of Dominators 116 10. 5. 4 Redundancy Identification 117 10. 6 Summary 119 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 11 POLYNOMIAL-TIME TESTABILITY 123 11. 1 Background 124 11. 1. 1 Fujiwara's Result 125 11. 1. 2 Contribution of the Present Work . . . . . . . . . 126 11. 2 Notation and Tenninology 127 11. 3 A Polynomial TlDle Algorithm 128 11. 3. 1 Primary Output Fault 129 11. 3. 2 Arbitrary Single Fault 135 11. 3. 3 Multiple Faults. . . . . . . . . . . . . . . . . . . 137 11. 4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . 139 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 ix 12 SPECIAL CASES OF HARD PROBLEMS 141 12. 1 Problem Statement 142 12. 2 Logic Simulation 143 12. 3 Logic Circuit Modeling . 146 12. 3. 1 Modelfor a Boolean Gate . . . . . . . . . . . . . 147 12. 3. 2 Circuit Modeling 148 12.