Verfügbarkeit: Logic synthesis and verification algorithms

Logic synthesis and verification algorithms:

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Bibliographische Detailangaben
Hauptverfasser:	Hachtel, Gary D. (VerfasserIn), Somenzi, Fabio (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York Springer 2006
Ausgabe:	1. softcover ed.
Schlagworte:	Algoritmos Circuitos integrados vlsi Circuitos lógicos Design Sistemas integrados em larga escala Álgebras de boole Datenverarbeitung Computer-aided design Integrated circuits > Verification Integrated circuits > Very large scale integration > Design > Data processing Logic design > Data processing Logischer Entwurf Logiksynthese
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XXXII, 564 S. Ill., graph. Darst.
ISBN:	0387310045 9780387310046

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents I Introduction 1 1 Introduction 5 1.1 VLSI: Opportunity and Challenge ................... . 5 1.1.1 Manufacturing Technology .................... 5 1.1.2 Design technology ....................... . 6 1.1.3 Why VLSI ............................. 7 1.2 VLSI Processes .............................. 7 1.3 Design Styles ............................... 8 1.3.1 Design Decomposition ...................... 8 1.3.2 Logic (Circuit) Design Styles .................. 10 1.4 Overview of Optimal Logic Synthesis .................. 14 1.4.1 Area-Time Tradeoff Curves ................... 15 1.4.2 The Technology Independent View — A Bit-Serial Full Adder Circuit ............................... 16 1.4.3 The Technology Dependent View — Technology Mapping ... 18 1.4.4 Testing — Is What I Fabricated What I Wanted? ....... 19 1.4.5 Graph Models and Finite State Machines ............ 21 1.4.6 Successors and Predecessors ................... 24 1.5 Graph Algorithms and Complexity ................... 24 1.5.1 Complexity ............................ 24 1.5.2 Computing the Product of Sets of Sets ............ . 26 1.5.3 Longest Paths ........................... 27 1.5.4 Backtracing ............................ 29 1.5.5 Complexity of Computing the Longest Path .......... 32 1.6 Asymptotic Complexity (or just complexity) .............. 33 1.6.1 Worst Case Asymptotic Upper Bound Complexity ....... 34 1.6.2 Complexity of Algorithms .................... 36 1.6.3 Practical Complexities ...................... 36 1.7 Brief Summary of MOS Device Behavior ................ 37 1.8 Notes .................................... 39 1.9 Summary ................................ . 39 1.10 Problems ................................. 39 A Quick Tour of Logic Synthesis with the Help of a Simple Example 47 2.1 A Simple Case Conversion Circuit .................... 47 2.2 First Refinement ............................. 49 2.3 The Transform Block ........................... 50 2.3.1 The CC Block .......................... . 52 2.3.2 An Optimized Transform Block ................. 53 2.4 The Command Interpreter ........................ 54 2.4.1 Checking for Equality ...................... 54 2.4.2 Optimizing the Command Interpreter .............. 54 2.5 Technology Mapping ........................... 57 2.6 Problems ................................. 58 II Two Level Logic Synthesis 73 3 Boolean Algebras 77 3.1 Sets, Relations, and Functions ...................... 77 3.1.1 Sets ................................ 77 3.1.2 Relations ............................. 79 3.1.3 Reflexive Binary Relations .................... 80 3.1.4 Functions ............................. 84 3.2 Partial Orders ............................... 85 3.2.1 Partially Ordered Sets ...................... 86 3.2.2 Hasse Diagrams .......................... 87 3.2.3 The Meet and Join Operations .................. 87 3.2.4 Totally Ordered Sets, Well-Ordered Sets, and Induction .... 89 3.2.5 Lattices .............................. 90 3.2.6 Definition of Boolean Algebras .................. 92 3.2.7 Examples and Properties of Boolean Algebras ......... 92 3.3 Boolean Functions ............................ 95 3.3.1 Boolean Formulae ......................... 96 3.3.2 Boolean Functions ........................ 97 3.3.3 Boole s Expansion Theorem ................... 98 3.3.4 The Minterm Canonical Form .................. 99 3.3.5 Pseudo-Boolean Functions .................... 101 3.3.6 The Boolean Algebra of ra-variable Boolean Functions ..... 101 3.3.7 Atoms of a Boolean Algebra ................... 101 3.4 Don t Care Conditions as Boolean Function Algebra Intervals .... 103 3.4.1 Satisfiability Don t Care Conditions ............... 104 3.4.2 Observability Don t Care Conditions .............. 105 3.4.3 Deriving Don t Cares From and Interval Specification ..... 106 3.5 Incomplete Specification of Boolean Functions ............. 106 3.5.1 Incompletely Specified Switching Functions ........... 106 3.5.2 Incompletely Specified Boolean Functions ........... 107 3.6 Notes .................................... 108 3.7 Summary ................................. 108 3.8 Problems ................................. 108 4 Synthesis of Two-Level Circuits 127 4.1 Design Optimality ............................ 127 4.2 Two-Level Logic ............................. 129 4.2.1 Cost Functions for Two-Level Implementations ......... 130 4.2.2 Minimality and Testability .................... 131 4.3 Sums of Products and Products of Sums ................ 132 4.4 Implicante and Prime Implicante ..................... 134 4.4.1 Quine s Prime Implicant Theorem ................ 134 4.5 Iterated Consensus ............................ 134 4.5.1 Consensus and Implications: A Digression ........... 135 4.5.2 The Tabular Method of Computing the Prime Implicante . . . 135 4.5.3 Iterated Consensus in General .................. 137 4.6 Recursive Computation of Prime Implicante .............. 138 4.7 Selecting a Subset of Primes ....................... 141 4.8 The Unate Covering Problem ...................... 143 4.8.1 Reduction Techniques ...................... 146 4.8.2 Essential Columns or Variables ................. 146 4.8.3 Row or Constraint Dominance .................. 146 4.8.4 Column or Variable Dominance ................. 147 4.8.5 Systematically Exploring the Search Space ........... 148 4.8.6 Computation of the Lower Bound ................ 149 4.9 The Branch-and-Bound Algorithm .................... 152 4.9.1 Choice of the Splitting Variable ................. 154 4.9.2 Examples of Splitting and Lower Bounding ........... 155 4.9.3 The Unate Covering Problem as an Integer Linear Program . 160 4.10 Multiple Output Functions ........................ 160 4.10.1 Multiple-Output Primes ..................... 161 4.10.2 Formulating the Covering Problem ............... 163 4.10.3 Incompletely Specified Multiple-Output Functions ....... 163 4.11 Notes .................................... 164 4.12 Summary ................................. 165 4.13 Problems ................................. 165 5 Heuristic Minimization of Two-Level Circuits 185 5.1 Local Search ................................ 185 5.1.1 Local Search Applied to Logic Minimization .......... 187 5.1.2 A Simple Local Search Algorithm for Logic Minimization . . . 190 5.2 Checking for Equivalence and Tautology ................ 191 5.2.1 Unate Functions . . . ....................... 194 5.2.2 Additional Speed-Up Techniques for Tautology Checking . . . 197 5.2.3 Examples of Tautology Checks . ................. 199 5.3 Choosing the Right Direction ...................... 200 5.3.1 Recursive Complementation ................... 201 5.3.2 Using the OFF-set in the Expansion .............. 203 5.4 Identifying Essential Primes ....................... 203 5.5 Multiple-Valued Logics .......................... 204 5.6 Notes .................................... 205 5.7 Summary ................................. 206 5.8 Problems ................................. 206 Binary Decision Diagrams (BDDs) 219 6.1 Representing Logic Functions with BDDs ................ 220 6.1.1 Binary Decision Diagrams by Way of Examples ........ 220 6.1.2 Formal Definition of BDDs .................... 222 6.1.3 How to Build the BDD for ƒ................... 225 6.1.4 Reduced BDDs .......................... 226 6.1.5 Why Ordering is Important ................... 230 6.2 Design Considerations for a BDD Package ............... 231 6.3 Algorithms ................................ 233 6.3.1 The ITE Algorithm ........................ 234 6.3.2 Complement Edges ........................ 237 6.3.3 The Computed Table ....................... 238 6.3.4 Conditioning of the ITE Calls .................. 238 6.3.5 The ITE-CONSTANT Algorithm ................. 240 6.4 Notes .................................... 243 6.5 Summary ................................. 244 6.6 Problems ................................. 244 III Models of Sequential Systems 251 7 Models of Sequential Systems 255 7.1 Introduction to Finite State Machines .................. 255 7.2 Synthesis of Finite State Machines .................... 257 7.3 FSMs: Definitions, Notation, and Examples .............. 261 7.3.1 Examples ............................. 261 7.3.2 Incomplete Specification ..................... 263 7.4 FSM Minimization for Completely Specified Machines ......... 265 7.4.1 Identifying the Equivalent States of an FSM .......... 265 7.4.2 State Equivalence Checking: the Partition/Refinement Approach269 7.4.3 Finding the Reduced Machine .................. 272 7.4.4 Moore Machines and DFAs ................... 272 7.4.5 The Iterative Collapsing Approach ............... 273 7.4.6 Summary of State Equivalence Checking Methods ....... 275 7.5 Graph Algorithms for FSM Traversal ................. . 275 7.5.1 Graphs, Subgraphs, and Components .............. 276 7.5.2 Graph Traversal — Breadth First Search ............ 278 7.5.3 Traversal — Depth First Search ................. 280 7.5.4 Finding the SCCs of a Directed Graph ............. 282 7.5.5 Shortest Paths .......................... 286 7.6 Models of Sequential Systems ...................... 289 7.7 FSTs: Strings, Runs, Reachability and Products ............ 292 7.7.1 Finite State Transition Structures ................ 292 7.7.2 NFAs and e-moves ........................ 295 7.7.3 FSTs as Labeled Digraphs.................... 295 7.7.4 Strings, Tapes and Runs of FSTs ................ 297 7.7.5 Product of FSTs ......................... 298 7.8 FSM Equivalence Checking ....................... 300 7.8.1 Strings which Distinguish Two Machines ............ 300 7.8.2 Building the Product Machine .................. 301 7.8.3 Equivalence Identification by Isomorphism ........... 305 7.9 Reachability Analysis ........................... 305 7.9.1 FSM Traversal Using Binary Decision Diagrams ........ 305 7.10 Symbolic FSM State Traversal ...................... 308 7.10.1 Transition Relations and Symbolic Image Computation .... 308 7.11 Notes. ................................... 312 7.12 Summary ................................. 313 7.13 Problems ................................. 313 Synthesis and Verification of Finite State Machines 325 8.1 Minimization of Incompletely Specified Machines ........... 325 8.1.1 Finding the Compatible Pairs ................... 328 8.1.2 Finding the Maximal Compatibles ................ 329 8.1.3 Finding the Prime Compatibles .................. 329 8.1.4 Setting up the Covering Problem ................. 332 8.1.5 Forming the Reduced Table ................... 334 8.2 The Binate Covering Problem ...................... 335 8.2.1 Formulation of BCP ....................... 337 8.2.2 Reduction Techniques ...................... 337 8.2.3 Choice of the Splitting Variable and Bounding ......... 340 8.2.4 Maximal independent set ..................... 340 8.2.5 Choice of the branching column .................. 341 8.2.6 Infeasible problems ......................... 341 8.2.7 An Example of Reductions .................... 342 8.3 State Encoding ..............................343 8.3.1 Practical Encoding Algorithms ................. 343 8.4 Decomposition and Encoding ...................... 347 8.4.1 Partitions .............................348 8.4.2 Partitions with Substitution Property .............. 350 8.4.3 Computation of the S.P. Partitions ............... 352 8.4.4 General Decomposition and State Encoding .......... 354 8.5 Notes. .................................. . 356 8.6 Notes. ................................... 357 8.7 Summary ................................. 357 8.8 Problems ................................. 357 9 Finite Automata 369 9.1 Finite Automata and Regular Languages ................ 370 9.1.1 String Acceptance ........................ 372 9.1.2 Languages of Finite Automata .................. 373 9.1.3 Complements of Languages ................... 376 9.1.4 Examples ............................. 377 9.2 DFA Synthesis .............................. 378 9.2.1 Determinization of FSTs and FAs ................ 383 9.2.2 The Subset Construction ..................... 383 9.2.3 The Deterministic Image ..................... 385 9.3 ω -Regular Automata ........................... 387 9.4 Formal Verification with ¿-Automata .................. 390 9.4.1 ω -Regular Languages ....................... 390 9.5 ω- regular Language Containment .................... 392 9.5.1 Lifting Acceptance Conditions to a Product L-Automaton . . 393 9.5.2 Example of Product L-Automaton ................ 393 9.5.3 BDD Representation of Cycle Sets and Recur Edges ...... 394 9.5.4 The Language Containment Algorithm ............. 395 9.5.5 Example of Containment Check ................. 396 9.6 Notes .................................... 397 9.7 Summary ................................. 397 9.8 Problems ................................. 398 IV Multilevel Logic Synthesis 405 10 Multi-Level Logic Synthesis 409 10.1 Introduction ................................ 409 10.1.1 Networksand Algebraic Operations ............... 410 10.2 Representation Issues and Choices .................... 412 10.2.1 Alternate Node Representations ................. 413 10.3 Representing Switching Functions in Factored Form .......... 417 10.3.1 Factored Forms .......................... 417 10.3.2 Algebraic and Boolean Expressions ............... 418 10.3.3 Algebraic and Boolean Factored Forms ............. 419 10.3.4 Value of a Factorization ..................... 420 10.3.5 Equivalent, Maximal, and Optimum Factorizations ...... 420 10.3.6 Size, Unateness, and Cofactors of a Factored Form ...... 422 10.4 Division .................................. 422 10.5 Kernels and Co-Kernels .......................... 425 10.5.1 Computation of Co-Kernels and Kernels ............ 427 10.6 Heuristic Factoring Algorithms ..................... 428 10.6.1 Generic Factoring Algorithm ................... 429 10.6.2 Quick Factor ........................... 433 10.6.3 Good Factor ............................ 434 10.6.4 Boolean Factor .......................... 434 10.6.5 Summary of Factoring Algorithms ................ 435 10.6.6 Rectangle Covering ........................ 436 10.7 Decomposition and Restructuring .................... 436 10.7.1 Algebraic Resubstitution ..................... 436 10.7.2 Selective Node Elimination .................... 437 10.7.3 Extraction ............................. 439 10.8 Notes .................................... 440 10.9 Summary ................................ . 441 10. lOProblems ................................. 441 11 Multi-Level Minimization 455 11.1 Introduction ................................ 455 11.2 Boolean Networks ............................. 456 11.2.1 Network Cost ........................... 459 11.3 Don t Cares in Multi-Level Networks .................. 461 11.3.1 Satisfiability Don t Cares ..................... 461 11.3.2 Observability Don t Cares .................... 462 11.3.3 Use of Don t Cares in Minimization ............... 462 11.3.4 Internal and External Don t Cares .............. . 463 11.3.5 External Satisfiability Don t Care Conditions .......... 463 11.3.6 External Observability Don t Care Conditions ......... 463 11.4 Internal Satisfiability Don t Cares .................... 464 11.5 Observability Don t Cares ........................ 465 11.5.1 Computing ODCs with the Boolean Difference ......... 468 11.6 Prime and Irredundant Networks .................... 468 11.7 Two-Level Minimization with Multi- Level Don t Cares ........ 469 11.8 Notes .................................... 470 11.9 Summary ................................. 470 ll.lOProblems ................................. 471 12 Automatic Test Generation for Combinational Circuits 475 12.1 Introduction ................................ 475 12.2 Faults and Fault Models ......................... 476 12.3 Automatic Test Generation ........................ 478 12.3.1 Excitation and Sensitization ................... 478 12.3.2 A Simple Test Generation Algorithm .............. 481 12.3.3 Implications and Backtracking ................. . 483 12.3.4 Choice of the Decision Variables ................. 486 12.3.5 Putting the Pieces Together ................... 488 12.4 Redundancy Removal ........................... 488 12.5 Notes. ................................... 492 12.6 Summary ................................. 492 12.7 Problems ................................. 492 13 Technology Mapping 505 13.1 Graph Covering and Technology Mapping ............... 506 13.2 Choice of Base Functions ......................... 507 13.3 Creating the Subject Graph ....................... 508 13.4 The DAG-Covering Problem ....................... 509 13.5 Tree Covering by Dynamic Programming ................ 509 13.6 Decomposition .............................. 512 13.7 Delay Optimization and Graph Covering ................ 513 13.8 Notes .................................... 514 13.9 Summary ................................. 514 ІЗ.ЮРгоЬіетз ................................. 515 A ASCII Codes 523 В Supplementary Problems 525 Bibliography 537 Index 555
adam_txt	Contents I Introduction 1 1 Introduction 5 1.1 VLSI: Opportunity and Challenge . . 5 1.1.1 Manufacturing Technology . 5 1.1.2 Design technology . . 6 1.1.3 Why VLSI . 7 1.2 VLSI Processes . 7 1.3 Design Styles . 8 1.3.1 Design Decomposition . 8 1.3.2 Logic (Circuit) Design Styles . 10 1.4 Overview of Optimal Logic Synthesis . 14 1.4.1 Area-Time Tradeoff Curves . 15 1.4.2 The Technology Independent View — A Bit-Serial Full Adder Circuit . 16 1.4.3 The Technology Dependent View — Technology Mapping . 18 1.4.4 Testing — Is What I Fabricated What I Wanted? . 19 1.4.5 Graph Models and Finite State Machines . 21 1.4.6 Successors and Predecessors . 24 1.5 Graph Algorithms and Complexity . 24 1.5.1 Complexity . 24 1.5.2 Computing the Product of Sets of Sets . . 26 1.5.3 Longest Paths . 27 1.5.4 Backtracing . 29 1.5.5 Complexity of Computing the Longest Path . 32 1.6 Asymptotic Complexity (or just complexity) . 33 1.6.1 Worst Case Asymptotic Upper Bound Complexity . 34 1.6.2 Complexity of Algorithms . 36 1.6.3 Practical Complexities . 36 1.7 Brief Summary of MOS Device Behavior . 37 1.8 Notes . 39 1.9 Summary . . 39 1.10 Problems . 39 A Quick Tour of Logic Synthesis with the Help of a Simple Example 47 2.1 A Simple Case Conversion Circuit . 47 2.2 First Refinement . 49 2.3 The Transform Block . 50 2.3.1 The CC Block . . 52 2.3.2 An Optimized Transform Block . 53 2.4 The Command Interpreter . 54 2.4.1 Checking for Equality . 54 2.4.2 Optimizing the Command Interpreter . 54 2.5 Technology Mapping . 57 2.6 Problems . 58 II Two Level Logic Synthesis 73 3 Boolean Algebras 77 3.1 Sets, Relations, and Functions . 77 3.1.1 Sets . 77 3.1.2 Relations . 79 3.1.3 Reflexive Binary Relations . 80 3.1.4 Functions . 84 3.2 Partial Orders . 85 3.2.1 Partially Ordered Sets . 86 3.2.2 Hasse Diagrams . 87 3.2.3 The Meet and Join Operations . 87 3.2.4 Totally Ordered Sets, Well-Ordered Sets, and Induction . 89 3.2.5 Lattices . 90 3.2.6 Definition of Boolean Algebras . 92 3.2.7 Examples and Properties of Boolean Algebras . 92 3.3 Boolean Functions . 95 3.3.1 Boolean Formulae . 96 3.3.2 Boolean Functions . 97 3.3.3 Boole's Expansion Theorem . 98 3.3.4 The Minterm Canonical Form . 99 3.3.5 Pseudo-Boolean Functions . 101 3.3.6 The Boolean Algebra of ra-variable Boolean Functions . 101 3.3.7 Atoms of a Boolean Algebra . 101 3.4 Don't Care Conditions as Boolean Function Algebra Intervals . 103 3.4.1 Satisfiability Don't Care Conditions . 104 3.4.2 Observability Don't Care Conditions . 105 3.4.3 Deriving Don't Cares From and Interval Specification . 106 3.5 Incomplete Specification of Boolean Functions . 106 3.5.1 Incompletely Specified Switching Functions . 106 3.5.2 Incompletely Specified Boolean Functions . 107 3.6 Notes . 108 3.7 Summary . 108 3.8 Problems . 108 4 Synthesis of Two-Level Circuits 127 4.1 Design Optimality . 127 4.2 Two-Level Logic . 129 4.2.1 Cost Functions for Two-Level Implementations . 130 4.2.2 Minimality and Testability . 131 4.3 Sums of Products and Products of Sums . 132 4.4 Implicante and Prime Implicante . 134 4.4.1 Quine 's Prime Implicant Theorem . 134 4.5 Iterated Consensus . 134 4.5.1 Consensus and Implications: A Digression . 135 4.5.2 The Tabular Method of Computing the Prime Implicante . . . 135 4.5.3 Iterated Consensus in General . 137 4.6 Recursive Computation of Prime Implicante . 138 4.7 Selecting a Subset of Primes . 141 4.8 The Unate Covering Problem . 143 4.8.1 Reduction Techniques . 146 4.8.2 Essential Columns or Variables . 146 4.8.3 Row or Constraint Dominance . 146 4.8.4 Column or Variable Dominance . 147 4.8.5 Systematically Exploring the Search Space . 148 4.8.6 Computation of the Lower Bound . 149 4.9 The Branch-and-Bound Algorithm . 152 4.9.1 Choice of the Splitting Variable . 154 4.9.2 Examples of Splitting and Lower Bounding . 155 4.9.3 The Unate Covering Problem as an Integer Linear Program . 160 4.10 Multiple Output Functions . 160 4.10.1 Multiple-Output Primes . 161 4.10.2 Formulating the Covering Problem . 163 4.10.3 Incompletely Specified Multiple-Output Functions . 163 4.11 Notes . 164 4.12 Summary . 165 4.13 Problems . 165 5 Heuristic Minimization of Two-Level Circuits 185 5.1 Local Search . 185 5.1.1 Local Search Applied to Logic Minimization . 187 5.1.2 A Simple Local Search Algorithm for Logic Minimization . . . 190 5.2 Checking for Equivalence and Tautology . 191 5.2.1 Unate Functions . . .'. 194 5.2.2 Additional Speed-Up Techniques for Tautology Checking . . . 197 5.2.3 Examples of Tautology Checks . . 199 5.3 Choosing the Right Direction . 200 5.3.1 Recursive Complementation . 201 5.3.2 Using the OFF-set in the Expansion . 203 5.4 Identifying Essential Primes . 203 5.5 Multiple-Valued Logics . 204 5.6 Notes . 205 5.7 Summary . 206 5.8 Problems . 206 Binary Decision Diagrams (BDDs) 219 6.1 Representing Logic Functions with BDDs . 220 6.1.1 Binary Decision Diagrams by Way of Examples . 220 6.1.2 Formal Definition of BDDs . 222 6.1.3 How to Build the BDD for ƒ. 225 6.1.4 Reduced BDDs . 226 6.1.5 Why Ordering is Important . 230 6.2 Design Considerations for a BDD Package . 231 6.3 Algorithms . 233 6.3.1 The ITE Algorithm . 234 6.3.2 Complement Edges . 237 6.3.3 The Computed Table . 238 6.3.4 Conditioning of the ITE Calls . 238 6.3.5 The ITE-CONSTANT Algorithm . 240 6.4 Notes . 243 6.5 Summary . 244 6.6 Problems . 244 III Models of Sequential Systems 251 7 Models of Sequential Systems 255 7.1 Introduction to Finite State Machines . 255 7.2 Synthesis of Finite State Machines . 257 7.3 FSMs: Definitions, Notation, and Examples . 261 7.3.1 Examples . 261 7.3.2 Incomplete Specification . 263 7.4 FSM Minimization for Completely Specified Machines . 265 7.4.1 Identifying the Equivalent States of an FSM . 265 7.4.2 State Equivalence Checking: the Partition/Refinement Approach269 7.4.3 Finding the Reduced Machine . 272 7.4.4 Moore Machines and DFAs . 272 7.4.5 The Iterative Collapsing Approach . 273 7.4.6 Summary of State Equivalence Checking Methods . 275 7.5 Graph Algorithms for FSM Traversal . . 275 7.5.1 Graphs, Subgraphs, and Components . 276 7.5.2 Graph Traversal — Breadth First Search . 278 7.5.3 Traversal — Depth First Search . 280 7.5.4 Finding the SCCs of a Directed Graph . 282 7.5.5 Shortest Paths . 286 7.6 Models of Sequential Systems . 289 7.7 FSTs: Strings, Runs, Reachability and Products . 292 7.7.1 Finite State Transition Structures . 292 7.7.2 NFAs and e-moves . 295 7.7.3 FSTs as Labeled Digraphs. 295 7.7.4 Strings, Tapes and Runs of FSTs . 297 7.7.5 Product of FSTs . 298 7.8 FSM Equivalence Checking . 300 7.8.1 Strings which Distinguish Two Machines . 300 7.8.2 Building the Product Machine . 301 7.8.3 Equivalence Identification by Isomorphism . 305 7.9 Reachability Analysis . 305 7.9.1 FSM Traversal Using Binary Decision Diagrams . 305 7.10 Symbolic FSM State Traversal . 308 7.10.1 Transition Relations and Symbolic Image Computation . 308 7.11 Notes. . 312 7.12 Summary . 313 7.13 Problems . 313 Synthesis and Verification of Finite State Machines 325 8.1 Minimization of Incompletely Specified Machines . 325 8.1.1 Finding the Compatible Pairs . 328 8.1.2 Finding the Maximal Compatibles . 329 8.1.3 Finding the Prime Compatibles . 329 8.1.4 Setting up the Covering Problem . 332 8.1.5 Forming the Reduced Table . 334 8.2 The Binate Covering Problem . 335 8.2.1 Formulation of BCP . 337 8.2.2 Reduction Techniques . 337 8.2.3 Choice of the Splitting Variable and Bounding . 340 8.2.4 Maximal independent set . 340 8.2.5 Choice of the branching column . 341 8.2.6 Infeasible problems . 341 8.2.7 An Example of Reductions . 342 8.3 State Encoding .343 8.3.1 Practical Encoding Algorithms . 343 8.4 Decomposition and Encoding . 347 8.4.1 Partitions .348 8.4.2 Partitions with Substitution Property . 350 8.4.3 Computation of the S.P. Partitions . 352 8.4.4 General Decomposition and State Encoding . 354 8.5 Notes. . . 356 8.6 Notes. . 357 8.7 Summary . 357 8.8 Problems . 357 9 Finite Automata 369 9.1 Finite Automata and Regular Languages . 370 9.1.1 String Acceptance . 372 9.1.2 Languages of Finite Automata . 373 9.1.3 Complements of Languages . 376 9.1.4 Examples . 377 9.2 DFA Synthesis . 378 9.2.1 Determinization of FSTs and FAs . 383 9.2.2 The Subset Construction . 383 9.2.3 The Deterministic Image . 385 9.3 ω -Regular Automata . 387 9.4 Formal Verification with ¿-Automata . 390 9.4.1 ω -Regular Languages . 390 9.5 ω- regular Language Containment . 392 9.5.1 Lifting Acceptance Conditions to a Product L-Automaton . . 393 9.5.2 Example of Product L-Automaton . 393 9.5.3 BDD Representation of Cycle Sets and Recur Edges . 394 9.5.4 The Language Containment Algorithm . 395 9.5.5 Example of Containment Check . 396 9.6 Notes . 397 9.7 Summary . 397 9.8 Problems . 398 IV Multilevel Logic Synthesis 405 10 Multi-Level Logic Synthesis 409 10.1 Introduction . 409 10.1.1 Networksand Algebraic Operations . 410 10.2 Representation Issues and Choices . 412 10.2.1 Alternate Node Representations . 413 10.3 Representing Switching Functions in Factored Form . 417 10.3.1 Factored Forms . 417 10.3.2 Algebraic and Boolean Expressions . 418 10.3.3 Algebraic and Boolean Factored Forms . 419 10.3.4 Value of a Factorization . 420 10.3.5 Equivalent, Maximal, and Optimum Factorizations . 420 10.3.6 Size, Unateness, and Cofactors of a Factored Form . 422 10.4 Division . 422 10.5 Kernels and Co-Kernels . 425 10.5.1 Computation of Co-Kernels and Kernels . 427 10.6 Heuristic Factoring Algorithms . 428 10.6.1 Generic Factoring Algorithm . 429 10.6.2 Quick Factor . 433 10.6.3 Good Factor . 434 10.6.4 Boolean Factor . 434 10.6.5 Summary of Factoring Algorithms . 435 10.6.6 Rectangle Covering . 436 10.7 Decomposition and Restructuring . 436 10.7.1 Algebraic Resubstitution . 436 10.7.2 Selective Node Elimination . 437 10.7.3 Extraction . 439 10.8 Notes . 440 10.9 Summary . . 441 10. lOProblems . 441 11 Multi-Level Minimization 455 11.1 Introduction . 455 11.2 Boolean Networks . 456 11.2.1 Network Cost . 459 11.3 Don't Cares in Multi-Level Networks . 461 11.3.1 Satisfiability Don't Cares . 461 11.3.2 Observability Don't Cares . 462 11.3.3 Use of Don't Cares in Minimization . 462 11.3.4 Internal and External Don't Cares . . 463 11.3.5 External Satisfiability Don't Care Conditions . 463 11.3.6 External Observability Don't Care Conditions . 463 11.4 Internal Satisfiability Don't Cares . 464 11.5 Observability Don't Cares . 465 11.5.1 Computing ODCs with the Boolean Difference . 468 11.6 Prime and Irredundant Networks . 468 11.7 Two-Level Minimization with Multi- Level Don't Cares . 469 11.8 Notes . 470 11.9 Summary . 470 ll.lOProblems . 471 12 Automatic Test Generation for Combinational Circuits 475 12.1 Introduction . 475 12.2 Faults and Fault Models . 476 12.3 Automatic Test Generation . 478 12.3.1 Excitation and Sensitization . 478 12.3.2 A Simple Test Generation Algorithm . 481 12.3.3 Implications and Backtracking . . 483 12.3.4 Choice of the Decision Variables . 486 12.3.5 Putting the Pieces Together . 488 12.4 Redundancy Removal . 488 12.5 Notes. . 492 12.6 Summary . 492 12.7 Problems . 492 13 Technology Mapping 505 13.1 Graph Covering and Technology Mapping . 506 13.2 Choice of Base Functions . 507 13.3 Creating the Subject Graph . 508 13.4 The DAG-Covering Problem . 509 13.5 Tree Covering by Dynamic Programming . 509 13.6 Decomposition . 512 13.7 Delay Optimization and Graph Covering . 513 13.8 Notes . 514 13.9 Summary . 514 ІЗ.ЮРгоЬіетз . 515 A ASCII Codes 523 В Supplementary Problems 525 Bibliography 537 Index 555
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spelling	Hachtel, Gary D. Verfasser aut Logic synthesis and verification algorithms by Gary D. Hachtel ; Fabio Somenzi 1. softcover ed. New York Springer 2006 XXXII, 564 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algoritmos larpcal Circuitos integrados vlsi larpcal Circuitos lógicos larpcal Design larpcal Sistemas integrados em larga escala larpcal Álgebras de boole larpcal Datenverarbeitung Computer-aided design Integrated circuits Verification Integrated circuits Very large scale integration Design Data processing Logic design Data processing Logischer Entwurf (DE-588)4168051-0 gnd rswk-swf Logiksynthese (DE-588)4348178-4 gnd rswk-swf Logischer Entwurf (DE-588)4168051-0 s DE-604 Logiksynthese (DE-588)4348178-4 s Somenzi, Fabio Verfasser aut Erscheint auch als Online-Ausgabe 0-387-31005-3 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014721301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Hachtel, Gary D. Somenzi, Fabio Logic synthesis and verification algorithms Algoritmos larpcal Circuitos integrados vlsi larpcal Circuitos lógicos larpcal Design larpcal Sistemas integrados em larga escala larpcal Álgebras de boole larpcal Datenverarbeitung Computer-aided design Integrated circuits Verification Integrated circuits Very large scale integration Design Data processing Logic design Data processing Logischer Entwurf (DE-588)4168051-0 gnd Logiksynthese (DE-588)4348178-4 gnd
subject_GND	(DE-588)4168051-0 (DE-588)4348178-4
title	Logic synthesis and verification algorithms
title_auth	Logic synthesis and verification algorithms
title_exact_search	Logic synthesis and verification algorithms
title_exact_search_txtP	Logic synthesis and verification algorithms
title_full	Logic synthesis and verification algorithms by Gary D. Hachtel ; Fabio Somenzi
title_fullStr	Logic synthesis and verification algorithms by Gary D. Hachtel ; Fabio Somenzi
title_full_unstemmed	Logic synthesis and verification algorithms by Gary D. Hachtel ; Fabio Somenzi
title_short	Logic synthesis and verification algorithms
title_sort	logic synthesis and verification algorithms
topic	Algoritmos larpcal Circuitos integrados vlsi larpcal Circuitos lógicos larpcal Design larpcal Sistemas integrados em larga escala larpcal Álgebras de boole larpcal Datenverarbeitung Computer-aided design Integrated circuits Verification Integrated circuits Very large scale integration Design Data processing Logic design Data processing Logischer Entwurf (DE-588)4168051-0 gnd Logiksynthese (DE-588)4348178-4 gnd
topic_facet	Algoritmos Circuitos integrados vlsi Circuitos lógicos Design Sistemas integrados em larga escala Álgebras de boole Datenverarbeitung Computer-aided design Integrated circuits Verification Integrated circuits Very large scale integration Design Data processing Logic design Data processing Logischer Entwurf Logiksynthese
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014721301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT hachtelgaryd logicsynthesisandverificationalgorithms AT somenzifabio logicsynthesisandverificationalgorithms

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