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1 Introduction.- 1.1 Scope of the Work.- 1.2 Organization of the Book.- 2 Fundamentals.- 2.1 Normal Galois Forms in Logic Synthesis.- 2.2 Invariant Multi-Valued Families of Generalized Spectral Tranforms.- 2.2.1 General Notation for Operations on Transform Matrices.- 2.2.2 Invariant Families of Multi-Valued Spectral Transforms.- 2.3 Summary.- 3 New Multiple-Valued S/D Trees and their Canonical Galois Field Sum-Of-Product Forms.- 3.1 Green/Sasao Hierarchy of Binary Canonical Forms.- 3.2 Binary S/D Trees and their Inclusive Forms.- 3.3 Ternary S/D Trees and their Inclusive Forms and Generalized Inclusive Forms.- 3.3.1 Ternary S/D Trees and Inclusive Forms.- 3.3.2 Enumeration of Ternary Inclusive Forms.- 3.4 Properties of TIFs and TGIFs.- 3.4.1 Properties of TIFs.- 3.4.2 Properties of TGIFs.- 3.5 An Extended Green/Sasao Hierarchy with a New Sub-Family for Ternary Reed-Muller Logic.- 3.6 Quaternary S/D Trees.- 3.7 An Evolutionary Algorithm for the Minimization of GFSOP Expressions Using IF Polarity from Multiple-Valued S/D Trees.- 3.8 Summary.- 4 Novel Methods For the Synthesis of Boolean and Multiple-Valued Logic Circuits Using Lattice Structures.- 4.1 Symmetry Indices.- 4.2 Fundamental (2,2) Two-Dimensional Lattice Structures.- 4.3 (3,3) Two-Dimensional Lattice Structures.- 4.4 New Three-Valued Families of (3,3) Three-Dimensional Shannon and Davio Lattice Structures.- 4.4.1 Three-Dimensional Lattice Structures.- 4.4.2 New (3,3) Three-Dimensional Invariant Shannon Lattice Structures.- 4.4.3 New (3,3) Three-Dimensional Invariant Davio Lattice Structures.- 4.5 An Algorithm for the Expansion of Ternary Functions Into (3,3) Three-Dimensional Lattice Structures.- 4.6 Example of the Implementation of Ternary Functions Using the New Three-Dimensional Lattice Structures.- 4.7 ISID: Iterative Symmetry Indices Decomposition.- 4.8 Summary.- 5 Reversible Logic: Fundamentals and New Results.- 5.1 Fundamental Reversible Logic Primitives and Circuits.- 5.2 The Elimination of Garbage in Two-Valued Reversible Circuits.- 5.3 Combinational Reversible Circuits.- 5.4 Novel General Methodology for the Creation and Classification of New Families of Reversible Invariant Multi-Valued Shannon and Davio Spectral Transforms.- 5.5 The Elimination of Garbage in Multiple-Valued Reversible Circuits.- 5.6 Summary.- 6 Reversible Lattice Structure.- 6.1 A General Algorithm for the Creation of Two-Valued and Multiple-Valued Reversible Lattice Structures.- 6.2 Summary.- 7 Novel Reconstructability Analysis Structures and their Reversible Realizations.- 7.1 New Type of Reconstructability Analysis: Two-Valued Modified Reconstructability Analysis (MRA).- 7.2 Multiple-Valued MRA.- 7.3 Reversible MRA.- 7.4 Summary.- 8 New Reversible Structures: Reversible Nets, Reversible Decision Diagrams, and Reversible Cascades.- 8.1 Reversible Nets.- 8.2 Reversible Decision Diagrams.- 8.3 Reversible Cascades.- 8.3.1 The Realization of GFSOP Expressions Using Reversible Cascades.- 8.4 Summary.- 9 Initial Evaluation of the New Reversible Logic Synthesis Methodologies.- 9.1 Complete Examples.- 9.2 Initial Comparison.- 9.3 Summary.- 10 Quantum Logic Circuits for Reversible Structures.- 10.1 Notation for Two-Valued and Multiple-Valued Quantum Circuits.- 10.2 Quantum Circuits.- 10.3 Summary.- 11 Quantum Computing: Basics and New Results.- 11.1 Fundamentals of Two-Valued Quantum Evolution Processes and Synthesis.- 11.1.1 Mathematical Decompositions for Quantum.- 11.2 New Two-Valued Quantum Evolution Processes.- 11.3 Novel Representations for Two-Valued Quantum Logic: Two-Valued Quantum Decision Trees and Diagrams.- 11.4 Fundamentals of Multiple-Valued Quantum Computing.- 11.5 New Multiple-Valued Quantum Chrestenson Evolution Process, Quantum Composite Basis States, and the Multiple-Valued Einstein-Podolsky-Rosen (EPR) Basis States.- 11.6 New Multiple-Valued Quantum Evolution Processes, Generalized Permuters, and their Circuit Analysis.- 11.7 Novel Representations for Multiple-Valued Quan

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