Structural Theory of Automata, Semigroups, and Universal Algebra

1. Front Matter

   Pages i-xxii

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2. Profinite semigroups and applications

   • Jorge Almeida

   Pages 1-45

3. The structure of free algebras

   • Joel Berman

   Pages 47-76

4. Completeness of automaton mappings with respect to equivalence relations

   • Jürgen Dassow

   Pages 77-108

5. Completeness of uniformly delayed operations

   • Teruo Hikita, Ivo G. Rosenberg

   Pages 109-147

6. Classification in finite model theory: counting finite algebras

   • Paweł M. Idziak

   Pages 149-158

7. Syntactic semigroups and the finite basis problem

   • Marcel Jackson

   Pages 159-167

8. Endoprimal algebras

   • Kalle Kaarli, László Márki

   Pages 169-180

9. The complexity of constraint satisfaction: an algebraic approach

   • Andrei Krokhin, Andrei Bulatov, Peter Jeavons

   Pages 181-213

10. On the automata functional systems

    • V. B. Kudryavtsev

    Pages 215-240

11. Algebra of behavior transformations and its applications

    • Alexander Letichevsky

    Pages 241-272

12. Congruence modular varieties: commutator theory and its uses

    • Ralph Mckenzie, John Snow

    Pages 273-329

13. Epigroups

    • Lev N. Shevrin

    Pages 331-380

14. Algebraic classifications of regular tree languages

    • Magnus Steinby

    Pages 381-432

15. Back Matter

    Pages 433-434

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Several of the contributions to this volume bring forward many mutually beneficial interactions and connections between the three domains of the title. Developing them was the main purpose of the NATO ASI summerschool held in Montreal in 2003. Although some connections, for example between semigroups and automata, were known for a long time, developing them and surveying them in one volume is novel and hopefully stimulating for the future. Another aspect is the emphasis on the structural theory of automata that studies ways to contstruct big automata from small ones. The volume also has contributions on top current research or surveys in the three domains. One contribution even links clones of universal algebra with the computational complexity of computer science. Three contributions introduce the reader to research in the former East block.

• algebra
• model theory
• semigroup
• transformation

• Department of Mathematical Theory of Intelligent Systems, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow, Russia

  Valery B. Kudryavtsev

• University of Montreal, Quebec, Canada

  Ivo G. Rosenberg

• Department of Mathematics and Statistics, University of Montreal, Quebec, Canada

  Martin Goldstein

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