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E-raamat: Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook

, (University of Calgary, Alberta, Canada), (University of Calgary, Alberta, Canada),
  • Formaat: 952 pages
  • Ilmumisaeg: 03-Oct-2018
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781420037586
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Decision Diagram Techniques for Micro- and Nanoelectronic Design HandbookSuurem pilt
  • Formaat: 952 pages
  • Ilmumisaeg: 03-Oct-2018
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781420037586
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This handbook sets out the theory and practice of decision diagrams (DDs) as applied to the representation and manipulation of logic functions, focusing on the use of DDs for analysis and design of micro- and nanoelectronic integrated circuits (nanoICs). Material is organized in four parts consisting of self-contained chapters written in a tutorial style. Selected methods of logic design are presented using decision diagrams, the central role of topological models is discused, and novel techniques of advanced logic design are presented with respect to new possibilities of processing in spatial dimensions. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

Decision diagram (DD) techniques are very popular in the electronic design automation (EDA) of integrated circuits, and for good reason. They can accurately simulate logic design, can show where to make reductions in complexity, and can be easily modified to model different scenarios.

Presenting DD techniques from an applied perspective, Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook provides a comprehensive, up-to-date collection of DD techniques. Experts with more than forty years of combined experience in both industrial and academic settings demonstrate how to apply the techniques to full advantage with more than 400 examples and illustrations. Beginning with the fundamental theory, data structures, and logic underlying DD techniques, they explore a breadth of topics from arithmetic and word-level representations to spectral techniques and event-driven analysis. The book also includes abundant references to more detailed information and additional applications.

Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook collects the theory, methods, and practical knowledge necessary to design more advanced circuits and places it at your fingertips in a single, concise reference.
Preface xxv
I FUNDAMENTALS OF DECISION DIAGRAM TECHNIQUES 1(238)
1 Introduction
3(18)
1.1 Data structures for the representation of discrete functions
3(6)
1.1.1 Switching theory
5(3)
1.1.2 Multivalued functions
8(1)
1.2 Decision tables
9(1)
1.3 Graphical data structures
10(1)
1.4 Spectral techniques
11(5)
1.4.1 Group theory
11(1)
1.4.2 Abstract Fourier analysis
12(3)
1.4.3 Correlation analysis
15(1)
1.5 Stochastic models and information theoretic measures
16(2)
1.5.1 Stochastic models and probability
16(1)
1.5.2 Information theoretical measures of logic functions and decision trees
17(1)
1.6 CAD of micro- and nanoelectronic circuits
18(1)
1.7 Further reading
19(2)
2 Data Structures
21(16)
2.1 Introduction
21(1)
2.2 Truth tables
22(1)
2.3 Algebraic representations
23(2)
2.3.1 Algebraic structure
23(1)
2.3.2 Matrix representation
24(1)
2.4 AND-OR expressions
25(2)
2.4.1 Sum-of-products expressions
25(1)
2.4.2 Computing the SOP coefficients
25(1)
2.4.3 Restoration
26(1)
2.5 Relevance to other data structures
27(5)
2.5.1 Dataflow graphs
28(1)
2.5.2 Hypercube
28(2)
2.5.3 Decision trees and diagrams
30(1)
2.5.4 Direct acyclic graph
31(1)
2.6 Relationship of data structures
32(2)
2.7 Further reading
34(3)
3 Graphical Data Structures
37(42)
3.1 Introduction
37(1)
3.2 Graphs
38(5)
3.3 Decision trees
43(9)
3.3.1 Tree-like graphs
43(2)
3.3.2 H-trees
45(1)
3.3.3 Definition of a decision tree
45(4)
3.3.4 Definition of a binary decision diagram
49(1)
3.3.5 Measures on decision trees and diagrams
50(2)
3.4 Shape of decision diagrams
52(8)
3.5 Embedding decision trees and diagrams into various topological structures
60(2)
3.6 Examples with hierarchical FPGA configuration
62(1)
3.7 Voronoi diagrams and Delaunay triangulations
63(9)
3.7.1 Voronoi diagram
64(5)
3.7.2 Delaunay tessellation
69(2)
3.7.3 Decision diagrams and Delaunay tessellation
71(1)
3.8 Further reading
72(7)
4 AND-EXOR Expressions, Trees, and Diagrams
79(40)
4.1 Introduction
79(1)
4.2 Terminology and classification of AND-EXOR, expressions
80(3)
4.3 Algebraic representation
83(10)
4.3.1 Positive polarity Reed-Muller expressions
84(5)
4.3.2 Fixed polarity
89(2)
4.3.3 Linear Reed-Muller expressions
91(2)
4.4 Graphical representation
93(9)
4.4.1 Hyp er cub e representation
94(1)
4.4.2 Decision trees using AND-EXOR, operations
95(5)
4.4.3 Decision diagrams
100(2)
4.5 Transeunt triangle representation
102(1)
4.6 Triangle topology
102(10)
4.6.1 Representation of a symmetric function
105(2)
4.6.2 Measures of transeunt triangle structures
107(2)
4.6.3 Transeunt triangles and decision trees
109(2)
4.6.4 Using transeunt triangles for representation of multivalued functions
111(1)
4.7 Further reading
112(7)
5 Arithmetic Representations
119(16)
5.1 Introduction
119(1)
5.2 Algebraic description
120(6)
5.2.1 General algebraic form
120(1)
5.2.2 Computing the coefficients
120(1)
5.2.3 Data flowgraphs
121(1)
5.2.4 Restoration
122(2)
5.2.5 Useful rules
124(1)
5.2.6 Polarity
124(2)
5.3 Graphical representations
126(6)
5.3.1 Hypercube representation
126(1)
5.3.2 Decision trees and diagrams
127(2)
5.3.3 Structural properties
129(3)
5.3.4 Decision diagram reduction
132(1)
5.4 Further reading
132(3)
6 Word - Level Representations
135(22)
6.1 Introduction
135(4)
6.2 Arithmetic word-level computation in matrix form
139(6)
6.2.1 Application of direct and inverse arithmetic transforms to word-level expressions
139(4)
6.2.2 Arithmetic word-level form in a given polarity
143(1)
6.2.3 Taylor representation
144(1)
6.3 Computing word-level expressions in the form of corteges
145(9)
6.3.1 Algebra of corteges
145(1)
6.3.2 Implementation of algebra of corteges
146(6)
6.3.3 Orthogonal corteges
152(2)
6.4 Further reading
154(3)
7 Spectral Techniques
157(22)
7.1 Introduction
157(1)
7.2 Spectral transforms
158(6)
7.2.1 Fourier transforms on finite groups
159(1)
7.2.2 Discrete Walsh transform
160(4)
7.3 Haar and related transforms
164(3)
7.4 Computing spectral coefficients
167(5)
7.4.1 Computing the Walsh coefficients
167(1)
7.4.2 Computing the Haar coefficients
168(4)
7.5 Discrete wavelet transforms
172(1)
7.6 Further reading
172(7)
8 Information - Theoretical Measures
179(30)
8.1 Introduction
179(1)
8.2 Information-theoretical measures
180(8)
8.2.1 Quantity of information
180(2)
8.2.2 Conditional entropy and relative information
182(2)
8.2.3 Entropy of a variable and a function
184(2)
8.2.4 Mutual information
186(2)
8.3 Information measures of elementary switching function of two variables
188(3)
8.4 Information-theoretical measures and symmetry
191(5)
8.4.1 Entropy of distribution of values of logic function
193(1)
8.4.2 Condition of symmetry over the distribution
194(2)
8.5 Information and flexibility
196(4)
8.5.1 Sets of pairs of functions to be distinguished
197(1)
8.5.2 Concept of neighborhood of a, function in terms of information
198(2)
8.6 Further reading
200(9)
9 Event - Driven Analysis
209(30)
9.1 Introduction
209(1)
9.2 Formal definition of change in a binary system
210(12)
9.2.1 Detection of change
210(3)
9.2.2 Matrix model of change
213(2)
9.2.3 Model for simultaneous change
215(2)
9.2.4 Model of multiple change: k-ordered Boolean differences
217(2)
9.2.5 Boolean difference with respect to a vector of variables in matrix form
219(1)
9.2.6 Symmetric properties of Boolean difference
220(2)
9.3 Generating Reed Muller expressions with logic Taylor series
222(1)
9.4 Computing Boolean differences on decision diagrams
222(5)
9.4.1 Boolean difference and N-hypercube
223(1)
9.4.2 Boolean difference, Davio tree, and N-hypercube
223(4)
9.5 Models of logic networks in tennis of change
227(4)
9.5.1 Event-driven analysis of switching function properties: dependence, sensitivity, and fault detection
227(2)
9.5.2 Useful rules
229(2)
9.6 Other logic differential operators
231(4)
9.6.1 Models of directed changes in algebraic form
231(8)
9.6.2 Arithmetic: analogs of Boolean differences and logic Taylor expansion
239
9.7 Further reading
235(4)
II DECISION DIAGRAM TECHNIQUES FOR SWITCHING FUNCTIONS 239(340)
10 Introduction
241(20)
10.1 Genesis and evolution of decision diagrams
241(3)
10.2 Various aspects of the construction of decision diagrams
244(5)
10.3 Applications of decision diagrams
249(3)
10.4 Implementation and technologies
252(5)
10.5 Further reading
257(4)
11 Classification of Decision Diagrams
261(12)
11.1 Introduction
261(2)
11.2 Classification of decision diagrams with respect to constant nodes
263(2)
11.3 Classification of decision diagrams with respect to non-terminal nodes
265(1)
11.4 Classification of decision diagrams with respect to decomposition rules
266(1)
11.5 Classification of decision diagrams with respect to labels at the edges
267(4)
11.6 Further reading
271(2)
12 Variable Ordering in Decision Diagrams
273(20)
12.1 Introduction
273(2)
12.2 Adjacent variable interchange
275(1)
12.3 Exact BDD minimization techniques
276(1)
12.4 Problem specific ordering techniques
277(2)
12.5 Dynamic variable ordering
279(2)
12.5.1 Window permutation
279(1)
12.5.2 Sifting
279(2)
12.6 Advanced techniques
281(4)
12.6.1 Symmetric variable and group sifting
281(2)
12.6.2 Linear sifting
283(1)
12.6.3 Window optimization
284(1)
12.7 Path length
285(1)
12.8 Reordering in BDD packages
286(1)
12.9 Further reading
287(6)
13 Spectral Decision Diagrams
293(12)
13.1 The theoretical background of spectral interpretation of decision diagram techniques
293(1)
13.2 Decision tree and spectrum of switching function
294(2)
13.3 Bases of spectral transforms and decision diagrams
296(1)
13.4 Fixed polarity spectral representations
296(4)
13.5 Spectral decision diagram techniques
300(3)
13.5.1 Decision diagrams as relations between algebraic and graphical data structures
302(1)
13.5.2 Bit-level and word-level strategy
303(1)
13.6 Further reading
303(2)
14 Linearly Transformed Decision Diagrams
305(24)
14.1 Introduction
305(2)
14.1.1 Affine transforms
306(1)
14.1.2 Linearly transformed decision diagrams
306(1)
14.2 Manipulation of variables using affine transforms
307(5)
14.2.1 Direct and inverse affine transforms
309(2)
14.2.2 Affine transforms of the adjacent variables
311(1)
14.3 Linearly transformed decision trees and diagrams
312(5)
14.3.1 Affine transforms in decision trees
313(1)
14.3.2 Affine transforms in decision diagrams
314(3)
14.4 Examples of linear transform techniques
317(2)
14.5 Further reading
319(10)
15 Decision Diagrams for Arithmetic Circuits
329(16)
15.1 Introduction
329(1)
15.2 Binary adders
329(4)
15.2.1 Full-adder
330(1)
15.2.2 Ripple-carry adder
330(1)
15.2.3 Binary-coded-decimal format
331(2)
15.3 Multipliers
333(3)
15.4 Word-level decision diagrams for arithmetic circuits
336(4)
15.4.1 Spectral diagrams for representation of arithmetical circuits
336(2)
15.4.2 Representation of adders by linear decision diagrams
338(2)
15.5 Further reading
340(5)
16 Edge - Valued Decision Diagrams
345(12)
16.1 Introduction
345(1)
16.2 Terminology and abbreviations of edge-valued decision trees and diagrams
346(3)
16.3 Spectra] interpretation of edge-valued decision diagrams
349(4)
16.3.1 Relationship of EVBDDs and Kronecker decision diagrams
352(1)
16.3.2 Factored edge-valued BDDs
352(1)
16.4 Binary moment diagrams
353(1)
16.4.1 Binary moment decision diagrams-*BMDs
353(1)
16.4.2 Arithmetic transform related decision diagrams
353(1)
16.4.3 Kronecker binary moment diagrams
354(1)
16.5 Further reading
354(3)
17 Word - Level Decision Diagrams
357(16)
17.1 Introduction
357(1)
17.2 Multiteruiinal decision trees and diagrams
358(2)
17.3 Spectral interpretation of word-level decision diagrams
360(1)
17.4 Binary moment trees and diagrams
361(5)
17.5 Haar spectral diagrams
366(2)
17.6 Haar spectral transform decision trees
368(1)
17.7 Other decision diagrams
369(1)
17.8 Further reading
369(4)
18 Minimization via Decision Diagrams
373(18)
18.1 Introduction
373(1)
18.2 Terminology
374(4)
18.3 Minimization using hypercubes
378(5)
18.4 Minimization of AND-EXOR expressions
383(4)
18.5 Further reading
387(4)
19 Decision Diagrams for Incompletely Specified Functions
391(22)
19.1 Introduction
391(1)
19.2 Representation of incompletely specified functions
392(2)
19.3 Decision diagrams for incompletely specified logic functions
394(5)
19.3.1 Safe BDD minimization
394(3)
19.3.2 Kleene function and ternary decision diagrams
397(2)
19.3.3 Manipulation of TDDs
399(1)
19.4 Incompletely specified decision diagrams
399(8)
19.4.1 Definition of the incompletely specified decision diagram
400(1)
19.4.2 Manipulation of incompletely specified decision diagrams
400(7)
19.5 Further reading
407(6)
20 Probabilistic Decision Diagram Techniques
413(16)
20.1 Introduction
413(1)
20.2 BDD methods for computing output probability
414(6)
20.2.1 A top-down approach
415(1)
20.2.2 A bottom-up approach
416(3)
20.2.3 Symbolic computation
419(1)
20.3 Cross-correlation of functions
420(6)
20.3.1 Recursive AND probability algorithm
422(2)
20.3.2 Modification of an algorithm
424(1)
20.3.3 Computing spectral coefficients
424(2)
20.4 Further reading
426(3)
21 Power Consumption Analysis using Decision Diagrams
429(18)
21.1 Introduction
429(2)
21.2 Switching activity
431(2)
21.3 Decision diagrams for power consumption estimation
433(8)
21.3.1 BDD for switching activity evaluation
434(2)
21.3.2 Information measures on BDDs arid switching activity
436(3)
21.3.3 Other decision diagrams for switching activity evaluation
439(2)
21.4 Further reading
441(6)
22 Formal Verification of Circuits
447(18)
22.1 Introduction
447(1)
22.2 Verification of combinational circuits
448(5)
22.3 Verification using other types of diagrams
453(5)
22.3.1 Word-level BDDs
455(2)
22.3.2 Boolean expression diagrams
457(1)
22.3.3 Non-canonical BDDs
458(1)
22.4 Verification of sequential circuits
458(2)
22.5 Further reading
460(5)
23 Ternary Decision Diagrams
465(16)
23.1 Terminology and abbreviations
465(2)
23.2 Definition of ternary decision trees
467(2)
23.3 EXOR ternary decision trees
469(1)
23.4 Bit-level ternary decision trees
469(2)
23.5 Word-level ternary decision trees
471(2)
23.6 Arithmetic transform ternary decision diagrams
473(1)
23.7 The relationships between arithmetic transform ternary decision diagrams and other decision trees
473(1)
23.8 Ternary decision diagrams and differential operators for switching functions
474(2)
23.9 Further reading
476(5)
24 Information - Theoretical Measures in Decision Diagrams
481(28)
24.1 Introduction
481(1)
24.2 Information-theoretical measures
481(3)
24.3 Information-theoretical measures in decision trees
484(8)
24.3.1 Decision tree induction
484
24.3.2 Information-theoretical notation of switching function expansion
24.3.3 Optimization of variable ordering in a decision tree
188(302)
24.3.4 Information measures in the N-hypercube
490(2)
24.4 Information-theoretical measures in multivalued functions
492(8)
24.4.1 Information notation of S expansion
493(2)
24.4.2 Information notations of pD and nD expansion
495(2)
24.4.3 Information criterion for decision tree design
497(1)
24.4.4 Remarks on information-theoretical measures in decision diagrams
498(2)
24.5 Ternary and pseudo-ternary decision trees
500(3)
24.6 Entropy-based minimization using pseudo-ternary trees
503(3)
24.7 Further reading
506(3)
25 Decomposition Using Decision Diagrams
509(36)
25.1 Introduction
509(4)
25.1.1 Covering strategy
510(1)
25.1.2 Decomposition strategy
511(2)
25.2 Decomposition types
513(5)
25.2.1 Shannon decomposition
513(1)
25.2.2 Davio decomposition
514(1)
25.2.3 Ashenhurst decomposition
514(2)
25.2.4 Curtis decomposition
516(1)
25.2.5 Bi-decomposition
516(2)
25.3 Decomposition based on BDD structure
518(8)
25.3.1 Multiplexer-based circuits
518(1)
25.3.2 Disjoint Ashenhurst decomposition
519(2)
25.3.3 Curtis decomposition
521(2)
25.3.4 Bi-decomposition
523(3)
25.4 Decomposition based on BDD operations
526(10)
25.4.1 Incompletely specified functions
527(1)
25.4.2 BBD based calculation of the m-fold minimum and m-fold maximum
528(2)
25.4.3 OR-bi-decomposition and AND-bi-decomposition
530(3)
25.4.4 EXOR-bi-decomposition
533(1)
25.4.5 Weak OR- and AND-bi-decomposition
534(2)
25.5 Further reading
536(9)
26 Complexity of Decision Diagrams
545(22)
26.1 Introduction
545(1)
26.2 Specific functions
546(3)
26.2.1 Basic logic functions
546(2)
26.2.2 Adders
548(1)
26.2.3 Multipliers and hidden weighted bit functions
548(1)
26.3 Bounds
549(3)
26.3.1 The general case
549(1)
26.3.2 Totally-symmetric functions
550(2)
26.3.3 Existence
552(1)
26.4 Complemented edges
552(2)
26.5 Path length
554(7)
26.5.1 Symmetric variable nodes
554(3)
26.5.2 Experimental results
557(1)
26.5.3 Longest path length oriented techniques
557(4)
26.6 Further reading
561(6)
27 Programming of Decision Diagrams
567(12)
27.1 Introduction
567(1)
27.2 Representation of nodes
568(1)
27.3 Representation of decision diagrams
568(1)
27.4 Construction of decision diagrams
569(4)
27.4.1 Unique table
572(1)
27.4.2 Computed table
572(1)
27.5 Construction of decision diagrams based on truth tables and variable ordering
573(2)
27.6 Calculations with decision diagrams
575(1)
27.7 Further reading
576(3)
III DECISION DIAGRAM TECHNIQUES FOR MULTIVALUED FUNCTIONS 579(90)
28 Introduction
581(14)
28.1 Multivalued logic
581(2)
28.2 Representation of multivalued functions
583(1)
28.3 Spectral theory of multivalued functions
584(2)
28.4 Multivalued decision trees and diagrams
586(2)
28.5 Further reading
588(7)
29 Multivalued Functions
595(18)
29.1 Introduction
595(1)
29.2 Multivalued functions
596(1)
29.3 Multivalued logic
596(6)
29.3.1 Operations of multivalued logic
597(4)
29.3.2 Multivalued algebras
601(1)
29.4 Galois fields
602(4)
29.4.1 Galois fields GF(m)
602(38)
29.4.2 Algebraic structure for Galois field representations
640
29.4.3 Galois field expansions
604(2)
29.4.4 Partial Galois field transforms
606(1)
29.5 Fault models based on the concept of change
606(4)
29.6 Further reading
610(3)
30 Spectral Transforms of Multivalued Functions
613(22)
30.1 Introduction
611(3)
30.2 Reed-Muller spectral transform
614(8)
30.2.1 Direct and inverse Reed Muller transforms
611(4)
30.2.2 Polarity
615(7)
30.3 Arithmetic transform
622(5)
30.3.1 Direct and inverse arithmetic transforms
699
30.3.2 Polarity
622(2)
30.3.3 Word-level representation
624(3)
30.4 Partial Reed-Muller-Fourier transforms
627(1)
30.5 Relation of spectral representations
627(2)
30.5.1 Families of spectral transforms
629(1)
30.5.2 Information about the behavior of logic functions in terms of change
629(1)
30.6 Further reading
629(6)
31 Classification of Multivalued Decision Diagrams
635(20)
31.1 Introduction
635(1)
31.2 Background theory
636(2)
31.3 Construction of EVDDs
638(5)
31.3.1 Motivation
640(1)
31.3.2 Algorithms
641(1)
31.3.3 Complexity
641(2)
31.3.4 Efficiency of EVDDs
643(1)
31.4 Illustrative examples
643(7)
31.5 Further reading
650(5)
32 Event - Driven Analysis in Multivalued Systems
655(14)
32.1 Introduction
655(1)
32.2 Multivalued difference
656(6)
32.3 Generation of Reed—Muller expressions
662(4)
32.3.1 Logic Taylor expansion of a multivalued function
662(1)
32.3.2 Computing Reed—Muller expressions
663(1)
32.3.3 Computing Reed—Muller expressions in matrix form
663(2)
32.3.4 N-hypercube representation
665(1)
32.4 Further reading
666(3)
IV SELECTED TOPICS OF DECISION DIAGRAM TECHNIQUES 669(220)
33 Introduction
671(14)
33.1 Relationship between decision diagrams and spatial structures
671(7)
33.1.1 Embedding decision trees and diagrams into different topologies
672(1)
33.1.2 Linear and multidimensional systolic arrays
673(5)
33.2 Decision diagrams for reversible computation
678(1)
33.3 Special types of decision diagrams and hybrid techniques
678(2)
33.4 Developing of new decision diagrams
680(1)
33.5 Further reading
680(5)
34 Three - Dimensional Techniques
685(34)
34.1 Introduction
685(2)
34.2 Spatial structures
687(2)
34.3 Hypercube data structure
689(5)
34.4 Assembling of hypercubes
694(2)
34.5 N-hypercube definition
696(6)
34.5.1 Extension of a hypercube
696(1)
34.5.2 Degree of freedom and rotation
697(1)
34.5.3 Coordinate description
698(4)
34.5.4 N-hypercube design for n > 3 dimensions
702(1)
34.6 Embedding a binary decision tree into an N-hypercube
702(5)
34.7 Spatial topological measurements
707(3)
34.8 Embedding decision diagrams into incomplete N-hypercubes
710(1)
34.8.1 Incomplete N-hypercubes
710(1)
34.8.2 Embedding technique
710(1)
34.9 Further reading
711(8)
35 Decision Diagrams in Reversible Logic
719(22)
35.1 Introduction
719(1)
35.2 Reversible and quantum circuits
720(9)
35.2.1 Reversible circuits
720(3)
35.2.2 Quantum circuits
723(6)
35.3 Decision diagram techniques
729(8)
35.3.1 Representing matrices as decision diagrams
731(3)
35.3.2 Matrix operations using decision diagrams
734(3)
35.4 Further reading
737(4)
36 Decision Diagrams on Quaternion Groups
741(16)
36.1 Terminology
742(1)
36.2 Introduction
743(1)
36.3 Group-theoretic approach to decision diagrams
744(4)
36.3.1 Decision diagrams for LUT FPGAs design
745(1)
36.3.2 Spectral interpretation
746(2)
36.4 Decision diagrams on quaternion group
748(11)
36.4.1 Fourier transform on Q2
748(1)
36.4.2 Decision diagrams on finite non-Abelian groups
749(1)
30.4.3 Decision diagrams on non-Abelian groups with pre-processing
750(1)
36.4.4 Advantages of non-Abelian groups in optimization of decision diagrams
751(8)
36.5 Further reading
759
37 Linear Word - Level Decision Diagrams
757(32)
37.1 Introduction
757(1)
37.2 Linearization
757(1)
37.3 Linear arithmetic expressions
758(5)
37.3.1 Grouping
758(2)
37.3.2 Computing the coefficients in the linear expression
760(1)
37.3.3 Weight assignment
761(1)
37.3.4 Masking
762(1)
37.4 Linear arithmetic expressions of elementary functions
763(4)
37.4.1 Functions of two and three variables
764(1)
37.4.2 AND, OR, and EXOR functions of n variables
765(1)
37.4.3 "Garbage" functions
766(1)
37.5 Linear decision diagrams
767(2)
37.6 Representation of a circuit level by linear word-level expression
769(3)
37.7 Linear decision diagrams for circuit representation
772(1)
37.8 Linear word-level expressions of multivalued functions
773(9)
37.8.1 Approach to linearization
774(1)
37.8.2 Algorithm for linearization of multivalued functions
775(2)
37.8.3 Manipulation of the linear model
777(2)
37.8.4 Library of linear models of multivalued gates
779(1)
37.8.5 Representation of a multilevel, multivalued circuit
780(1)
37.8.6 Linear decision diagrams
780(2)
37.8.7 Remarks on computing details
782(1)
37.9 Linear nonarithmetic word-level representation of multivalued functions
782(2)
37.9.1 Linear word-level for MAX expressions
782(2)
37.9.2 Network representation by linear models
784(1)
37.10 Further reading
784(5)
38 Fibonacci Decision Diagrams
789(20)
38.1 Introduction
789(1)
38.2 Terminology and abbreviations for Fibonacci decision trees and diagrams
790(4)
38.3 Generalized Fibonacci numbers and codes
794(1)
38.3.1 Fibonacci p-numbers
794(1)
38.3.2 Fibonacci p-codes
794(1)
38.4 Fibonacci decision trees
795(7)
38.4.1 Binary decision trees and multiterminal binary decision trees
795(4)
38.4.2 Properties of Fibonacci decision diagrams
799(3)
38.5 Fibonacci decision trees and contracted Fibonacci p-codes
802(1)
38.6 Spectral Fibonacci decision diagrams
803(2)
38.7 Further reading
805(4)
39 Techniques of Computing via Taylor - Like Expansions
809(36)
39.1 Terminology
810(2)
39.1.1 Additive structure of spectral coefficients
810(1)
39.1.2 Multiplicative structure of spectral coefficients
811(1)
39.1.3 Relationship of polynomial-like representations
811(1)
39.2 Computing Reed–Muller expressions
812(10)
39.2.1 Cube-based logic Taylor computing
815(4)
39.2.2 Properties of Boolean difference in cube notation
819(1)
39.2.3 Numerical example
820(1)
39.2.4 Matrix form of logic Taylor expansion
820(1)
39.2.5 Computing logic Taylor expansion by decision diagram
821(1)
39.3 Computing arithmetic expressions via arithmetic Taylor expansion
822(7)
39.3.1 Arithmetic analog of logic Taylor expansion
822(4)
39.3.2 Cube based arithmetic spectrum computing
826(1)
39.3.3 Properties of arithmetic differences in cube notation
826(1)
39.3.4 Matrix form of arithmetic Taylor expansion
827(2)
39.3.5 Computing arithmetic Taylor expansion by decision diagram
829(1)
39.4 Computing Walsh expressions via Taylor expansion
829(10)
39.4.1 Matrix form of Walsh differences
829(4)
39.4.2 Walsh differences in symbolic form
833(2)
39.4.3 Properties of Walsh differences in cube notation
835(2)
39.4.4 Computing Taylor expansion by decision diagram
837(2)
39.5 Further reading
839(6)
40 Developing New Decision Diagrams
845(22)
40.1 Introduction
845(1)
40.2 Spectral tools for generation of decision diagrams
845(12)
40.2.1 Approaches to the construction of decision diagrams
846(2)
40.2.2 The spectral approach
848(1)
40.2.3 Basic theorems
848(2)
40.2.4 Decision diagram and the spectrum of a switching function
850(7)
40.3 Group theoretic approach to designing decision diagrams
857(3)
40.3.1 Basic theorems
858(1)
40.3.2 Group-theoretic approach and topology
858(2)
40.4 Further reading
860(7)
41 Historical Perspectives and Open Problems
867(22)
41.1 Trends in decision diagram techniques
867(1)
41.2 New design and optimization strategies
867(7)
41.2.1 Bio-inspired strategies
869(1)
41.2.2 Adaptive reconfiguration
870(1)
41.2.3 Artificial intelligence
870(1)
41.2.4 Neural networks
871(1)
41.2.5 Flexibility
872(1)
41.2.6 Probabilistic techniques and information-theoretical measures
873(1)
41.3 Extension of the area of application
874(1)
41.3.1 Implementation aspects
874(1)
41.3.2 Topology and embedding properties
875(1)
41.4 Nanocircuit design - a new frontier for decision diagrams
875(1)
41.4.1 Modeling spatial dimensions
875(1)
41.4.2 Modeling spatial computing structures
875(1)
41.4.3 Modeling nanocomputing
876(1)
41.5 Further reading
876(13)
V APPENDIX 889(26)
Appendix A: Algebraic Structures for the Fourier Transform on Finite Groups
891(6)
Appendix B: Fourier Analysis on Groups
897(10)
Appendix C: Discrete Walsh Functions
907(6)
Appendix D: The Basic Operations for Ternary and Quaternary Logic
913(2)
Index 915


Yanushkevich, Svetlana N.; Miller, D. Michael; Shmerko, Vlad P.; Stankovic, Radomir S.
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