# Computational and Experimental Group Theory

Share this page *Edited by *
*Alexandre V. Borovik; Alexei G. Myasnikov*

Since its origin in the early 20th century, combinatorial
group theory has been primarily concerned with algorithms for solving
particular problems on groups given by generators and relations: word
problems, conjugacy problems, isomorphism problems, etc. Recent years
have seen the focus of algorithmic group theory shift from the
decidability/undecidability type of result to the complexity of
algorithms. Papers in this volume reflect that paradigm shift.

Articles are based on the AMS/ASL Joint Special Session, Interactions
Between Logic, Group Theory and Computer Science.

The volume is suitable for graduate students and research mathematicians
interested in computational problems of group theory.

#### Readership

Graduate students and research mathematicians interested in computational problems of group theory.

# Table of Contents

## Computational and Experimental Group Theory

- Contents v6 free
- Preface vii8 free
- Quantum algorithms in group theory 110 free
- Genetic algorithms and equations in free groups and semigroups 6372
- 1. Introduction 6372
- 2. A genetic algorithm framework on the free group 6675
- 3. Choosing problems 6978
- 4. Traceback 7079
- 5. Coevolution 7180
- 6. The genus problem and equations in a free semigroup 7382
- 7. The algorithm for the genus problem 7483
- 8. Discussion 7786
- 9. One more case study: restricted conjugacy problem in free partially commutative groups 7887
- References 8089

- One variable equations in free groups via context free languages 8392
- Whitehead method and genetic algorithms 8998
- The structure of automorphic conjugacy in the free group of rank two 115124
- Pattern recognition approaches to solving combinatorial problems in free groups 197206
- Experimenting with primitive elements in F2 215224