Sequential logic synthesis (Kluwer int'l series in engineering and computer science 162), Softcover reprint of the original 1st ed. 1992
The Springer International Series in Engineering and Computer Science Series, Vol. 162

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Sequential Logic Synthesis
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Sequential logic synthesis (Kluwer int'l series in engineering and computer science 162)
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226 p. · Hardback
3. 2 Input Encoding Targeting Two-Level Logic . . . . . . . . 27 3. 2. 1 One-Hot Coding and Multiple-Valued Minimization 28 3. 2. 2 Input Constraints and Face Embedding 30 3. 3 Satisfying Encoding Constraints . . . . . . . 32 3. 3. 1 Definitions . . . . . . . . . . . . . . . 32 3. 3. 2 Column-Based Constraint Satisfaction 33 3. 3. 3 Row-Based Constraint Satisfaction . . 37 3. 3. 4 Constraint Satisfaction Using Dichotomies . 38 3. 3. 5 Simulated Annealing for Constraint Satisfaction 41 3. 4 Input Encoding Targeting Multilevel Logic. . 43 3. 4. 1 Kernels and Kernel Intersections . . . 44 3. 4. 2 Kernels and Multiple-Valued Variables 46 3. 4. 3 Multiple-Valued Factorization. . . . . 48 3. 4. 4 Size Estimation in Algebraic Decomposition . 53 3. 4. 5 The Encoding Step . 54 3. 5 Conclusion . . . . . . . . . 55 4 Encoding of Symbolic Outputs 57 4. 1 Heuristic Output Encoding Targeting Two-Level Logic. 59 4. 1. 1 Dominance Relations. . . . . . . . . . . . . . . . 59 4. 1. 2 Output Encoding by the Derivation of Dominance Relations . . . . . . . . . . . . . . . . . . . . . 60 . . 4. 1. 3 Heuristics to Minimize the Number of Encoding Bits . . . . . . . . . . . . 64 4. 1. 4 Disjunctive Relationships . . . . . . . . . . . 65 4. 1. 5 Summary . . . . . . . . . . . . . . . . . . 66 . . 4. 2 Exact Output Encoding Targeting Two-Level Logic. 66 4. 2. 1 Generation of Generalized Prime Implicants . 68 4. 2. 2 Selecting a Minimum Encodeable Cover . . . 68 4. 2. 3 Dominance and Disjunctive Relationships to S- isfy Constraints . . . . . . . . . . . 70 4. 2. 4 Constructing the Optimized Cover 73 4. 2. 5 Correctness of the Procedure . . 73 4. 2. 6 Multiple Symbolic Outputs . . .
Acknowledgments.- 1 Introduction.- 1.1 Computer-Aided VLSI Design.- 1.2 The Synthesis Pipeline.- 1.3 Sequential Logic Synthesis.- 1.4 Early Work in Sequential Logic Synthesis.- 1.5 Recent Developments.- 1.5.1 State Encoding.- 1.5.2 Finite State Machine Decomposition.- 1.5.3 Sequential Don’t Cares.- 1.5.4 Sequential Resynthesis at the Logic Level.- 1.6 Organization of the Book.- 2 Basic Definitions and Concepts.- 2.1 Two-Valued Logic.- 2.2 Multiple-Valued Logic.- 2.3 Multilevel Logic.- 2.4 Multiple-Valued Input, Multilevel Logic.- 2.5 Finite Automata.- 3 Encoding of Symbolic Inputs.- 3.1 Introduction.- 3.2 Input Encoding Targeting Two-Level Logic.- 3.2.1 One-Hot Coding and Multiple-Valued Minimization.- 3.2.2 Input Constraints and Face Embedding.- 3.3 Satisfying Encoding Constraints.- 3.3.1 Definitions.- 3.3.2 Column-Based Constraint Satisfaction.- 3.3.3 Row-Based Constraint Satisfaction.- 3.3.4 Constraint Satisfaction Using Dichotomies.- 3.3.5 Simulated Annealing for Constraint Satisfaction.- 3.4 Input Encoding Targeting Multilevel Logic.- 3.4.1 Kernels and Kernel Intersections.- 3.4.2 Kernels and Multiple-Valued Variables.- 3.4.3 Multiple-Valued Factorization.- 3.4.4 Size Estimation in Algebraic Decomposition.- 3.4.5 The Encoding Step.- 3.5 Conclusion.- 4 Encoding of Symbolic Outputs.- 4.1 Heuristic Output Encoding Targeting Two-Level Logic.- 4.1.1 Dominance Relations.- 4.1.2 Output Encoding by the Derivation of Dominance Relations.- 4.1.3 Heuristics to Minimize the Number of Encoding Bits.- 4.1.4 Disjunctive Relationships.- 4.1.5 Summary.- 4.2 Exact Output Encoding Targeting Two-Level Logic.- 4.2.1 Generation of Generalized Prime Implicants.- 4.2.2 Selecting a Minimum Encodeable Cover.- 4.2.3 Dominance and Disjunctive Relationships to Sat-isfy Constraints.- 4.2.4 Constructing the Optimized Cover.- 4.2.5 Correctness of the Procedure.- 4.2.6 Multiple Symbolic Outputs.- 4.2.7 The Issue of the All Zeros Code.- 4.2.8 Reduced Prime Immplicant Table Generation.- 4.2.9 Covering with Encodeability Constraints.- 4.2.10 Experimental Results Using the Exact Algorithm.- 4.2.11 Computationally Efficient Heuristic Minimization.- 4.3 Symbolic Output Don’t Cares.- 4.4 Output Encoding for Multilevel Logic.- 4.5Conclusion.- 5 State Encoding.- 5.1 Heuristic State Encoding Targeting Two-Level Logic.- 5.1.1 Approximating State Encoding as Input Encoding.- 5.1.2 Constructing Input and Dominance Relations.- 5.1.3 Heuristics to Minimize the Number of Encoding Bits.- 5.1.4 Alternate Heuristic State Encoding Strategies.- 5.2 Exact State Encoding for Two-Level Logic.- 5.2.1 Generation of Generalized Prime Implicants.- 5.2.2 Selecting a Minimum Encodeable Cover.- 5.2.3 Constructing an Optimized Cover.- 5.2.4 Reduced Prime Implicant Table Generation.- 5.2.5 The Covering Step.- 5.2.6 Heuristics to Minimize the Number of Encoding Bits.- 5.2.7 Encoding Via Boolean Satisfiability.- 5.3 Symbolic Next State Don’t Cares.- 5.4 State Encoding for Multilevel Logic.- 5.4.1 Introduction.- 5.4.2 Modeling Common Cube Extraction.- 5.4.3 A Fanout-Oriented Algorithm.- 5.4.4 A Fanin-Oriented Algorithm.- 5.4.5 The Embedding Algorithm.- 5.4.6 Improvements to Estimation Strategies.- 5.5 Conclusion.- 6 Finite State Machine Decomposition.- 6.1 Introduction.- 6.2 Definitions for Decomposition.- 6.3 Preserved Covers and Partitions.- 6.4 General Decomposition Using Factors.- 6.4.1 Introduction.- 6.4.2 An Example Factorization.- 6.4.3 Defining An Exact Factor.- 6.4.4 Exact Factorization.- 6.4.5 Identifying Good Factors.- 6.4.6 Limitations of the Factoring Approach.- 6.5 Exact Decomposition Procedure for a Two-Way General Topology.- 6.5.1 The Cost Function.- 6.5.2 Formulation of Optimum Decomposition.- 6.5.3 Relationship to Partition Algebra.- 6.5.4 Relationship to Factorization.- 6.5.5 Generalized Prime Implicant Generation.- 6.5.6 Encodeability of a GPI Cover.- 6.5.7 Correctness of the Exact Algorithm.- 6.5.8 Checking for Output Constraint Violations.- 6.5.9 Checking for Input Constraint Violations.- 6.5.10 Relative Complexity of Encodeability Checking.- 6.5.11 The Covering Step in Exact Decomposition.- 6.6 Targeting Arbitrary Topologies.- 6.6.1 Cascade Decompositions.- 6.6.2 Parallel Decompositions.- 6.6.3 Arbitrary Decompositions.- 6.6.4 Exactness of the Decomposition Procedure.- 6.7 Heuristic General Decomposition.- 6.7.1 Overview.- 6.7.2 Minimization of Covers and Removal of Constraint Violations.- 6.7.3 Symbolic-expand.- 6.7.4 Symbolic-reduce.- 6.8 Relationship to State Assignment.- 6.9 Experimental Results.- 6.10 Conclusion.- 7 Sequential Don’t Cares.- 7.1 Introduction.- 7.2 State Minimization.- 7.2.1 Generating the Implication Table.- 7.2.2 Completely-Specified Machines.- 7.2.3 Incompletely-Specified Machines.- 7.2.4 Dealing with Exponentially-Sized Input Alphabets.- 7.3 Input Don’t Care Sequences.- 7.3.1 Input Don’t Care Vectors.- 7.3.2 Input Don’t Care Sequences to Minimize States.- 7.3.3 Exploiting Input Don’t Care Sequences.- 7.3.4 Early Work on Input Don’t Care Sequences.- 7.4 Output Don’t Cares to Minimize States.- 7.4.1 Exploiting Output Don’t Cares.- 7.5 Single Machine Optimization at the Logic Level.- 7.5.1 Introduction.- 7.5.2 Invalid State and Unspecified Edge Don’t Cares.- 7.5.3 Equivalent State Don’t Cares.- 7.5.4 Boolean Relations Due To Equivalent States.- 7.5.5 Minimization With Don’t Cares and Boolean Re-lations.- 7.6 Interconnected Machine Optimization at the Logic Level.- 7.6.1 Unconditional Compatibility.- 7.6.2 Conditional Compatibility.- 7.6.3 Invalid States and Edges.- 7.6.4 Searching for Unreachability and Compatibility.- 7.7 Conclusion.- 8 Conclusions and Directions for Future Work.- 8.1 Alternate Representations.- 8.2 Optimization at the Logic Level.- 8.3 Don’t Cares and Testability.- 8.4 Exploiting Register-Transfer Level Information.- 8.5 Sequential Logic Synthesis Systems.