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.

Synopsis

The three authors' idea is that in order to exploit the massive parallelism of neural networks one needs algorithms that will be quite different from the current problem solving methodology. They present new models for digital logic, solve problems of testing in several unconventional ways, and formulate solutions for graph theory problems. Annotat

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