Advances in Applications of Logincal Dynamic Systems:Ó¢ÎÄ

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