Preface

Chapter 1 Preliminaries
1��1 Semi-tensor Product of Matrices
1��2 Matrix Expression of Logical Functions
1��3 Summary of Finite State Machines

Chapter 2 Reachability of Finite Automata and Its Application
2��1 Introduction
2��2 Dynamic Equations of Finite Automata
2��3 Reachability Analysis of Finite Automata
2��4 Language Recognition of Finite Automata
2��5 Illustrative Examples
2��6 Conclusion

Chapter 3 Controllability and Stabilization of Finite Automata
3��1 Introduction
3��2 Controllability of Finite Automata
3��3 Stabilization of Finite Automata
3��4 Illustrative Examples
3��5 Conclusion

Chapter 4 Verification Analysis of Self-verifying Automata
4��1 Introduction
4��2 Bilinear State Transition Equations of Self-verifying Finite Automaton
4��3 Self-verifying Algorithms for Finite Automaton
4��4 Illustrative Examples
4��5 Conclusion

Chapter 5 Modelling and Control of Combined Finite Automata
5��1 Introduction
5��2 Composition of Finite Automata
5��3 Algebraic Construction of Combined Finite Automata
5��4 State and Output Control of Combined Finite Automata
5��5 Illustrative Examples
5��6 Conclusion

Chapter 6 Reachability Analysis of Discrete Event Dynamic Systems
6��1 Introduction
6��2 Mathematical Formulation of Logical Dynamics for Controlled Finite Automata
6��3 Algebraic Reachability Condition of Controlled Finite Automata
6��4 Algebraic Algorithm for Reachability of Controlled Finite Automata
6��5 Illustrative Examples
6��6 Conclusion

Chapter 7 Algebraic Method of Finding k-Degree and k-Balance Control Sets of Graphs
7��1 Introduction
7��2 Problem Statement
7��3 Algebraic Algorithm of Searching Control Sets of Graphs
7��4 Algebraic Algorithm of Searching k-Degree and k-Balance Control Sets of Graphs
7��5 Testing Examples
7��6 Conclusion

Chapter 8 Graph Approach to Solve k-Track Assignment Problem
8��1 Introduction
8��2 Searching k-internally Stable Sets of Graphs
8��3 Searching k-Absolute Maximum Internally Stable Sets of Graphs
8��4 Solvability of k-Track Assignment Problem
8��5 Illustrative Example
8��6 Conclusion

Chapter 9 Predictor Identification of Boolean Networks
9��1 Introduction
9��2 Judgment Criterion of Data-permitted Predictors
9��3 Logical Equations of Predictors
9��4 Solutions of Logical Equations
9��5 Identification of Predictors
9��6 Further Discussion on Predictors from Observed Data
9��7 Conclusion

Chapter 10 Algebraic Simplification of Boolean Networks
10��1 Introduction
10��2 Problem Description
10��3 Preserved Properties of Simplified Boolean Networks
10��4 Algebraic Algorithm of Finding Steady States and Cycles of Simplified Boolean Networks
10��5 Comparison with Other Methods
10��6 Testing Example
10��7 Conclusion