Graph algebras and automata /
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| Author / Creator: | Kelarev, A. V. (Andrei V.) |
|---|---|
| Imprint: | New York : Marcel Dekker, c2003. |
| Description: | viii, 366 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Monographs and textbooks in pure and applied mathematics ; 257 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4926252 |
Table of Contents:
- Preface
- 1. Preliminaries
- 1.1. Sets
- 1.2. Sequences
- 1.3. Functions or Mappings
- 1.4. Operations
- 1.5. Modular Arithmetic
- 1.6. Extended Euclidean Algorithm
- 1.7. Euler's Theorem and RSA Cryptosystem
- 1.8. Relations
- 1.9. Graphs
- 1.10. Exercises
- 2. Algebraic Structures
- 2.1. Words and Free Monoids
- 2.2. Groupoids
- 2.3. Semigroups and Monoids
- 2.4. Cayley Graphs
- 2.5. Groups
- 2.6. Commutative Semigroups
- 2.7. Rees Matrix Semigroups
- 2.8. Finite Semigroups
- 2.9. Lattices
- 2.10. Boolean Algebras
- 2.11. Rings
- 2.12. Fields and Vector Spaces
- 2.13. Polynomial Rings and Finite Fields
- 2.14. Matrix Rings
- 2.15. Linear Codes
- 2.16. Cyclic Codes
- 2.17. Universal Algebras
- 2.18. Exercises
- 3. Automata and Languages
- 3.1. Finite State Automata
- 3.2. Language Accepted by Automata
- 3.3. Operations on Languages, Regular Expressions
- 3.4. Algorithm 1: Language Accepted by FSA
- 3.5. Constructing Automata for Languages
- 3.6. Algorithm 2: Language Accepted by FSA
- 3.7. Minimization Algorithm
- 3.8. Syntactic and Transformation Monoids
- 3.9. Krohn-Rhodes Decomposition Theorem
- 3.10. Grammars and Rewriting Systems
- 3.11. Other Classes of Automata
- 3.12. Tree Languages
- 3.13. Exercises
- 4. Syntactic Monoids of Automata
- 5. Congruences on Automata
- 6. Minimal Automata
- 7. Languages
- 8. Tree Languages
- 9. Equational Theories
- 10. Groupoid Rings
- 11. Dualities, Topologies, Flatness
- 12. Open Problems
- Appendix A.. Glossary of Notation
- Bibliography
- Index
