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

• M. Batty, S. L. Braunstein, A. J. Duncan, and S. Rees -- Quantum algorithms in group theory
• R. F. Booth, D. Y. Bormotov, and A. V. Borovik -- Genetic algorithms and equations in free groups and semigroups
• R. H. Gilman and A. G. Myasnikov -- One variable equations in free groups via context free languages
• A. D. Miasnikov and A. G. Myasnikov -- Whitehead method and genetic algorithms
• B. Khan -- The structure of automorphic conjugacy in the free group of rank two
• R. M. Haralick, A. D. Miasnikov, and A. G. Myasnikov -- Pattern recognition approaches to solving combinatorial problems in free groups
• D. Y. Bormotov -- Experimenting with primitive elements in \(F_2\)