Rudiments of μ Calculus 1st Edition by A Arnold, D Niwinski ISBN 0585474338 9780585474335

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ISBN 10: 0585474338 
ISBN 13: 9780585474335
Author: A Arnold, D Niwinski

This book presents what in our opinion constitutes the basis of the theory of the mu-calculus, considered as an algebraic system rather than a logic. We have wished to present the subject in a unified way, and in a form as general as possible. Therefore, our emphasis is on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata, which we also explain in an algebraic way.

Rudiments of μ Calculus 1st Table of contents:

Section 1: Introduction to μ-Calculus
1.1 What is μ-Calculus?
1.2 Applications of μ-Calculus in Computer Science
1.3 Key Features of μ-Calculus
1.4 Historical Background and Development

Section 2: Basic Concepts and Notations
2.1 Modal Logic and Its Role in μ-Calculus
2.2 Syntax of μ-Calculus
    2.2.1 Modal Operators
    2.2.2 Fixed-Point Operators
2.3 Semantics of μ-Calculus
    2.3.1 Kripke Structures
    2.3.2 Truth Assignments
2.4 Formal Definition of μ-Calculus

Section 3: Fixed-Point Operators in μ-Calculus
3.1 Introduction to Fixed-Point Operators
3.2 μ and ν Operators
3.3 Existential and Universal Fixed Points
3.4 Interpreting Fixed-Point Formulas
3.5 Examples of Fixed-Point Applications

Section 4: Expressive Power of μ-Calculus
4.1 Comparison with Other Modal Logics
4.2 Expressing Properties of Transition Systems
4.3 μ-Calculus and Temporal Logic
4.4 Computation and Complexity of μ-Calculus

Section 5: Model Checking and Verification
5.1 Model Checking with μ-Calculus
5.2 Algorithms for μ-Calculus Model Checking
5.3 Automated Tools for μ-Calculus Verification
5.4 Case Study: μ-Calculus in Model Checking

Section 6: Advanced Topics in μ-Calculus
6.1 Fixed-Point Logic and Game Semantics
6.2 Higher-Order μ-Calculus
6.3 μ-Calculus and Automata Theory
6.4 Extensions and Variants of μ-Calculus

Section 7: Applications of μ-Calculus
7.1 Formal Verification of Software Systems
7.2 Verification of Security Protocols
7.3 μ-Calculus in Real-Time Systems
7.4 Applications in Reactive Systems

Section 8: Conclusion and Future Directions
8.1 Summary of μ-Calculus Fundamentals
8.2 Challenges and Open Problems
8.3 Future Trends in μ-Calculus Research

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Tags: A Arnold, D Niwinski, Calculus