Weighted Automata, Formal Power Series and Weighted Logic (BestMasters)

Acknowledgements
Abstract
Contents
1. Introduction
2. Languages, Automata and Monadic Second-Order Logic
	2.1. Words and Formal Languages
	2.2. Finite Automata
	2.3. Kleene\'s Theorem
	2.4. Monadic Second-Order Logic for Words
	2.5. The Büchi–Elgot–Trakhtenbrot Theorem
3. Weighted Automata
	3.1. Semirings and Formal Power Series
	3.2. Weighted Automata and Their Behavior
	3.3. Linear Representations
4. The Kleene–Schützenberger Theorem
	4.1. Operations on Formal Power Series
	4.2. Rational Formal Power Series
	4.3. The Kleene–Schützenberger Theorem
		Closure Properties of Recognizable Formal Power Series
		Weighted Automata and Linear Systems of Equations
5. Weighted Monadic Second-Order Logic and Weighted Automata
	5.1. Syntax and Semantics
	5.2. Results of Droste and Gastin
		From Weighted Formulas to Weighted Automata
		From Weighted Automata to Weighted Formulas
		Locally Finite Semirings
6. Summary and Further Research
	6.1. Summary
	6.2. Further Research
A. Appendix
	A.1. Model Theory and Monadic Second-Order Logic
	A.2. Monadic Second-Order Logic for Words
References
Index