Computational and experimental group theory : AMS-ASL joint special session, interactions between logic, group theory, and computer science, January 15-16, 2003, Baltimore, Maryland / / Alexandre V. Borovik, Alexei G. Myasnikov, editors

• Record Nr.: UNINA9910812588003321
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2004]; ©2004
• ISBN: 0-8218-7939-1; 0-8218-5684-7
• Descrizione fisica: 1 online resource (234 p.)
• Collana: Contemporary mathematics, , 0271-4132 ; ; 349
• Disciplina: 512/.21
• Soggetti: Permutation groups; Non-Abelian groups; Quantum theory - Mathematics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Preface""; ""Quantum algorithms in group theory""; ""1. Introduction""; ""2. The basics of quantum computing""; ""3. The Deutschâ€?Jozsa algorithm""; ""4. Shor's algorithm and factoring integers""; ""5. Grover's algorithm""; ""6. Watrous' algorithms for solvable groups""; ""References""; ""Genetic algorithms and equations in free groups and semigroups""; ""1. Introduction""; ""2. A genetic algorithm framework on the free group""; ""3. Choosing problems""; ""4. Traceback""; ""5. Coevolution""; ""6. The genus problem and equations in a free semigroup""; ""7. The algorithm for the genus problem""""8. Discussion""; ""9. One more case study: restricted conjugacy problem in free partially commutative groups""; ""References""; ""One variable equations in free groups via context free languages""; ""1. Introduction""; ""2. Results from Language Theory""; ""3. Proof of Theorem 1""; ""References""; ""Whitehead method and genetic algorithms""; ""1. Introduction""; ""2. Whitehead method""; ""3. Description of the genetic algorithm""; ""4. Experiments and results""; ""5. Time complexity of GWA""; ""6. ; Mathematical problems arising from the experiments""; ""References""""The structure of automorphic conjugacy in the free group of rank two""; ""1. The automorphism graph of F2""; ""2. Combinatorial groundwork""; ""3. The structure within levels""; ""4. Algorithmic applications""; ""5. Computational tools""; ""6. Conclusions and future work""; ""References""; ""Pattern recognition approaches to solving combinatorial problems in free groups""; ""1. Introduction""; ""2. General remarks on pattern recognition tasks""; ""3. Feature vectors""; ""4. Pattern recognition tools and models""; ""5. Recognizing Whitehead minimal words in free groups""; ""References""""Experimenting with primitive elements in F2""