Spectral Techniques in VLSI CAD

1 Introduction. - 1. 1 Motivation. - 1. 2 Background and History. - 1. 3 Mathematical Requirements. - 1. 4 Organization. - 2 The Boolean Domain. - 2. 1 Boolean Functions. - 2. 2 Pseudo-Boolean Functions. - 2. 3 Output Probability. - 2. 4 Summary. - 3 The Spectral Domain. - 3. 1 Spectra of Logic Functions. - 3. 2 Spectral Transforms. - 3. 3 Transform Procedures. - 3. 4 Relationships Between the Transforms. - 3. 5 Spectral Properties. - 3. 6 Summary. - 4 Decision Diagrams. - 4. 1 Decision Diagram Definitions. - 4. 2 Decision Diagram Varieties. - 4. 3 Bit-level Decompositions. - 4. 4 Word-level Decompositions. - 4. 5 Edge-valued Decision Diagrams. - 4. 6 Summary. - 5 Computation of Spectral Coefficients. - 5. 1 Cube List Approaches. - 5. 2 Methods Based on BDD Paths and Disjoint Cubes. - 5. 3 Spectral Computation Using Decision Diagrams. - 5. 4 Computation Based on Cayley Graphs. - 5. 5 Spectra of Incompletely-specified Functions. - 5. 6 Summary. - 6 BDD Minimization. - 6. 1 BDD Variable Ordering Techniques. - 6. 2 Probability Based Minimization. - 6. 3 Linear Transformations. - 6. 4 Summary. - 7 Logic Synthesis. - 7. 1 Spectral Translation. - 7. 2 Maximum Correlation Iterative Approach. - 7. 3 Synthesis Using Spectral Heuristics. - 7. 4 Technology Mapping. - 7. 5 Summary. - 8 Logic Verification. - 8. 1 Classical Approaches. - 8. 2 Signature Methods. - 8. 3 Subsets of Haar Coefficients for Equivalence Checking. - 8. 4 Summary. - 9 Concluding Remarks. - References. Language: English