Logic Functions and Equations: Fundamentals and Applications using the XBOOLE-Monitor

Description

Foreword Preface Contents Acronyms Part I XBOOLE 1 The Concepts of XBOOLE 1.1 Motivation and Aims 1.2 Ternary Matrix (TM) 1.3 Space Concept 1.4 Unlimited Number of Logic Variables 1.5 Memory Concept 1.6 Form Predicate of a Ternary Vector List 1.7 Sets and Ordered Sequences of Logic Variables 1.8 The XBOOLE-System: Management of TVLs and VTs 1.9 Parallel Computation of the Data Stored in TernaryVectors 1.10 The XBOOLE-Library 1.11 The XBOOLE-Monitor XBM 2 References 2 The XBOOLE-Monitor XBM 2 2.1 The Program Window of XBM 2 2.2 Basic Steps to Use XBM 2 2.3 Problem-Programs 2.4 An Overview About the Commands of XBM 2 2.5 Exercises 2.6 Solutions 2.7 Supplementary Exercises References Part II Fundamentals 3 Basic Algebraic Structures 3.1 The Roots of Logic Concepts 3.2 The Set B 3.3 Boolean Algebras 3.4 The Set Bn 3.5 Exercises 3.6 Solutions 3.7 Supplementary Exercises References 4 Logic Functions 4.1 Logic Functions 4.2 Formulas and Expressions 4.3 Special Logic Functions 4.4 Minimization Problems 4.5 Complete Systems of Logic Functions 4.6 Exercises 4.7 Solutions 4.8 Supplementary Exercises References 5 Logic Equations 5.1 Basic Problems and Definitions 5.2 Systems of Equations and Inequalities 5.3 Ternary Vectors as the Main Data Structure 5.4 The Solution of Simple Equations 5.5 Operations with Solution-Sets 5.6 Special Equation-Systems 5.7 Exercises 5.8 Solutions 5.9 Supplementary Exercises References 6 Boolean Differential Calculus 6.1 Preliminaries 6.2 Vectorial Derivative Operations 6.3 Single Derivative Operations 6.4 k-Fold Derivative Operations 6.5 Differential of a Boolean Variable 6.6 Differential Operations of Logic Functions 6.7 Exercises 6.8 Solutions 6.9 Supplementary Exercises References 7 Sets, Lattices, and Classes of Logic Functions 7.1 Partially Defined Functions—Lattices of Functions 7.2 Generalized Lattices of Logic Functions 7.3 Derivative Operations of Lattices of Logic Functions 7.4 Solution of Equations with Regard to Variables 7.5 Relations Between Lattices of Solution Functions 7.6 Functional Equations 7.7 Boolean Differential Equations 7.8 Exercises 7.9 Solutions 7.10 Supplementary Exercises References Part III Applications 8 Logic, Arithmetic, and Special Functions 8.1 Propositional Logic 8.2 Binary Arithmetic 8.3 Coding 8.4 Specific Normal Form 8.5 Most Complex Logic Functions 8.6 Bent Functions 8.7 Exercises 8.8 Solutions 8.9 Supplementary Exercises References 9 SAT-Problems 9.1 Specification and Solution Methods 9.2 Complexity and NP-Completeness 9.3 Placement Problems 9.4 Covering Problems 9.5 Path Problems 9.6 Coloring Problems 9.7 Exercises 9.8 Solutions 9.9 Supplementary Exercises References 10 Extremely Complex Problems 10.1 Rectangle-Free Four-Colored 10.2 Discussion of the Complexity 10.3 Basic Approaches and Results 10.4 Construction of Four-Colored Grids G16,16 and G16,20 10.5 Solution of All Four-Colored Grids up to 18 18 10.6 Solution of Four-Colored Grids with the Size 12 21 10.7 Exercises 10.8 Solutions 10.9 Supplementary Exercises References 11 Combinational Circuits 11.1 The Circuit Model 11.2 Analysis 11.3 Covering Methods for Synthesis 11.4 Decomposition Methods for Synthesis 11.5 Test 11.6 Exercises 11.7 Solutions 11.8 Supplementary Exercises References 12 Sequential Circuits 12.1 The Circuit Model 12.2 Analysis of Asynchronous Sequential Circuits 12.3 Analysis of Synchronous Sequential Circuits 12.4 Synthesis of Asynchronous Finite State Machines 12.5 Synthesis of Synchronous Finite State Machines 12.6 Hardware Software Co-design 12.7 Exercises 12.8 Solutions 12.9 Supplementary Exercises References Bibliography 1 The Concepts of XBOOLE 2 The XBOOLE-Monitor XBM 2 3 Basic Algebraic Structures 4 Logic Functions 5 Logic Equations 6 Boolean Differential Calculus 7 Sets, Lattices, and Classes of Logic Functions 8 Logic, Arithmetic, and Special Functions 9 SAT-Problems 10 Extremely Complex Problems 11 Combinational Circuits 12 Sequential Circuits Index