This book mainly introduces some recent advances in applications of logical dynamic systems. In particular， we concentrate on the applications in the fields of finite automata， graphs， operational research and Boolean networks. In the area of finite automata， we discuss the dynamical model， the reachability and eontroUability. In the theory of graph， we introduce an algebraic approach to study the structures of graphs， which is applied to solve the multi-track assignment problem in operational research. In the field of Boolean networks， the problems of predictor identification and simplification are fully considered.This book is suitable for professional researchers in the fields of control science and engineering， industrial automation， electrical automation and mechanical engineering， but also can be used as a reference material for relevant scientific and technical engineers.
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
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