Graph Algebras and Automata

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CRC Press, Jul 8, 2003 - Mathematics - 344 pages
Graph algebras possess the capacity to relate fundamental concepts of computer science, combinatorics, graph theory, operations research, and universal algebra. They are used to identify nontrivial connections across notions, expose conceptual properties, and mediate the application of methods from one area toward questions of the other four. After a concentrated review of the prerequisite mathematical background, Graph Algebras and Automata defines graph algebras and reveals their applicability to automata theory. It proceeds to explore assorted monoids, semigroups, rings, codes, and other algebraic structures and to outline theorems and algorithms for finite state automata and grammars.
 

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Contents

Preface
1
Algebraic Structures
39
Automata and Languages
143
Syntactic Monoids of Automata
219
Congruences on Automata
227
Minimal Automata
249
Languages
255
Tree Languages
283
Equational Theories
289
Groupoid Rings
311
Open Problems
321
Bibliography
329
Index
351
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About the author (2003)

Andrei Kelarev is a Senior Lecturer in Mathematics at the University of Tasmania, Hobart, Australia.

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