本書主要介紹邏輯動態(tài)系統(tǒng)在應用方面的最新研究進展，特別關注在下列領域的應用研究：有限自動機、圖論、運籌學與控制論以及布爾網(wǎng)絡等。在有限自動機領域，本書討論了自動機的動態(tài)建模問題、可達性問題及可控性問題。在圖論領域，本書重點介紹了利用邏輯系統(tǒng)的方法去研究圖的結構分析問題，以及圖的結構分解在運籌學中的應用，例如多軌道任務分配問題的可解性條件等。在布爾網(wǎng)絡方面，本書著重分析了布爾網(wǎng)絡預測集的辨識問題以及代數(shù)化簡等問題。本書適合控制科學與工程、工業(yè)自動化、系統(tǒng)科學、控制理論、數(shù)學、人工智能等專業(yè)的師生及科研人員閱讀參考，也可作為相關學科高年級本科生及研究生的教學參考用書。
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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