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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
| 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 |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (234 p.) |
| Disciplina | 512/.21 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Permutation groups
Non-Abelian groups Quantum theory - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-8218-7939-1
0-8218-5684-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Quantum algorithms in group theory""; ""1. Introduction""; ""2. The basics of quantum computing""; ""3. The Deutsch�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"" |
| Record Nr. | UNINA-9910480012603321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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
| 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 |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (234 p.) |
| Disciplina | 512/.21 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Permutation groups
Non-Abelian groups Quantum theory - Mathematics |
| ISBN |
0-8218-7939-1
0-8218-5684-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Quantum algorithms in group theory""; ""1. Introduction""; ""2. The basics of quantum computing""; ""3. The Deutsch�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"" |
| Record Nr. | UNINA-9910788667303321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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
| 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 |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (234 p.) |
| Disciplina | 512/.21 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Permutation groups
Non-Abelian groups Quantum theory - Mathematics |
| ISBN |
0-8218-7939-1
0-8218-5684-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Quantum algorithms in group theory""; ""1. Introduction""; ""2. The basics of quantum computing""; ""3. The Deutsch�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"" |
| Record Nr. | UNINA-9910812588003321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computational and statistical group theory : AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey / / Robert Gilman, Vladimir Shpilrain, Alexei G. Myasnikov, editors
| Computational and statistical group theory : AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey / / Robert Gilman, Vladimir Shpilrain, Alexei G. Myasnikov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (138 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory - Data processing
Finite groups - Data processing Combinatorial group theory - Data processing |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-8218-7888-3
0-8218-3158-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Uniform growth, actions on trees and GL2""; ""Centralisers of involutions in black box groups""; ""Measuring sets in infinite groups""; ""1. Introduction""; ""2. Conditions on a measure""; ""3. Atomic probability measures""; ""4. Kolmogorov complexity functions""; ""5. Kolmogorov complexity functions on finitely generated groups""; ""6. Short elements bias and behaviour at infinity""; ""7. Degrees of polynomial growth ""on average""""; ""8. Measures generated by random walks""; ""9. Behaviour of the induced measures on finite factor groups""
""10. The growth function and asymptotic density""""References""; ""Quantum one-way automata and finitely generated groups""; ""Spectral properties of a torsion-free weakly branch group defined by a three state automaton""; ""Malnormal subgroups of free groups""; ""Variants of product replacement""; ""Weakly amenable groups""; ""The Knuth-Bendix procedure for strings and large rewriting systems"" |
| Record Nr. | UNINA-9910480457903321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computational and statistical group theory : AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey / / Robert Gilman, Vladimir Shpilrain, Alexei G. Myasnikov, editors
| Computational and statistical group theory : AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey / / Robert Gilman, Vladimir Shpilrain, Alexei G. Myasnikov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (138 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory - Data processing
Finite groups - Data processing Combinatorial group theory - Data processing |
| ISBN |
0-8218-7888-3
0-8218-3158-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Uniform growth, actions on trees and GL2""; ""Centralisers of involutions in black box groups""; ""Measuring sets in infinite groups""; ""1. Introduction""; ""2. Conditions on a measure""; ""3. Atomic probability measures""; ""4. Kolmogorov complexity functions""; ""5. Kolmogorov complexity functions on finitely generated groups""; ""6. Short elements bias and behaviour at infinity""; ""7. Degrees of polynomial growth ""on average""""; ""8. Measures generated by random walks""; ""9. Behaviour of the induced measures on finite factor groups""
""10. The growth function and asymptotic density""""References""; ""Quantum one-way automata and finitely generated groups""; ""Spectral properties of a torsion-free weakly branch group defined by a three state automaton""; ""Malnormal subgroups of free groups""; ""Variants of product replacement""; ""Weakly amenable groups""; ""The Knuth-Bendix procedure for strings and large rewriting systems"" |
| Record Nr. | UNINA-9910788658003321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computational and statistical group theory : AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey / / Robert Gilman, Vladimir Shpilrain, Alexei G. Myasnikov, editors
| Computational and statistical group theory : AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey / / Robert Gilman, Vladimir Shpilrain, Alexei G. Myasnikov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (138 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory - Data processing
Finite groups - Data processing Combinatorial group theory - Data processing |
| ISBN |
0-8218-7888-3
0-8218-3158-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""Uniform growth, actions on trees and GL2""; ""Centralisers of involutions in black box groups""; ""Measuring sets in infinite groups""; ""1. Introduction""; ""2. Conditions on a measure""; ""3. Atomic probability measures""; ""4. Kolmogorov complexity functions""; ""5. Kolmogorov complexity functions on finitely generated groups""; ""6. Short elements bias and behaviour at infinity""; ""7. Degrees of polynomial growth ""on average""""; ""8. Measures generated by random walks""; ""9. Behaviour of the induced measures on finite factor groups""
""10. The growth function and asymptotic density""""References""; ""Quantum one-way automata and finitely generated groups""; ""Spectral properties of a torsion-free weakly branch group defined by a three state automaton""; ""Malnormal subgroups of free groups""; ""Variants of product replacement""; ""Weakly amenable groups""; ""The Knuth-Bendix procedure for strings and large rewriting systems"" |
| Record Nr. | UNINA-9910828539903321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors
| Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (186 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory
Mathematical statistics Cryptography |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-7950-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""On power- and commutation transitive, power commutative, and restricted Gromov groups""; ""Braid-based cryptography""; ""1. Background on braids""; ""1.1. Braid groups""; ""1.2. The greedy normal form""; ""1.3. Implementation of braids""; ""2. Braid-based schemes""; ""2.1. Key exchange""; ""2.2. Enciphering�deciphering""; ""2.3. Authentication""; ""2.4. Signature""; ""3. Attacks against the braid schemes""; ""3.1. Solutions to the Conjugacy Problem""; ""3.2. Attacks based on length""; ""3.3. Attacks based on linear representations""
""3.4. Are these attacks dangerous?""""4. Clues for further research""; ""4.1. Key generation""; ""4.2. Random drawing and security proofs""; ""4.3. Using braid words and braid reduction""; ""4.4. Hash functions""; ""4.5. Resorting to other braid problems""; ""5. Conclusion""; ""Discriminating and squarelike groups I: Axiomatics""; ""The density of small words in a free group is 0""; ""Braid groups and Aut(F2) are not rigid""; ""On varieties of groups in which all periodic groups are abelian""; ""Subgroups of fully residually free groups: algorithmic problems""; ""1. Introduction"" ""2. Preliminaries""""3. Intersection of two finitely generated subgroups of FZ[t]""; ""4. Properties of intersections of finitely generated subgroups of FZ[t]""; ""5. Centralizers in finitely generated fully residually free groups""; ""6. Conjugacy problem in finitely generated subgroups of FZ[t]""; ""References""; ""Weak hyperbolicity and free constructions""; ""Some properties of the conjugacy class growth function""; ""Boundary test elements""; ""Geodesics in the braid group on three strands""; ""Remarks on the growth of inverse semigroups"" ""Assessing security of some group based cryptosystems"" |
| Record Nr. | UNINA-9910480987303321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors
| Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (186 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory
Mathematical statistics Cryptography |
| ISBN | 0-8218-7950-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""On power- and commutation transitive, power commutative, and restricted Gromov groups""; ""Braid-based cryptography""; ""1. Background on braids""; ""1.1. Braid groups""; ""1.2. The greedy normal form""; ""1.3. Implementation of braids""; ""2. Braid-based schemes""; ""2.1. Key exchange""; ""2.2. Enciphering�deciphering""; ""2.3. Authentication""; ""2.4. Signature""; ""3. Attacks against the braid schemes""; ""3.1. Solutions to the Conjugacy Problem""; ""3.2. Attacks based on length""; ""3.3. Attacks based on linear representations""
""3.4. Are these attacks dangerous?""""4. Clues for further research""; ""4.1. Key generation""; ""4.2. Random drawing and security proofs""; ""4.3. Using braid words and braid reduction""; ""4.4. Hash functions""; ""4.5. Resorting to other braid problems""; ""5. Conclusion""; ""Discriminating and squarelike groups I: Axiomatics""; ""The density of small words in a free group is 0""; ""Braid groups and Aut(F2) are not rigid""; ""On varieties of groups in which all periodic groups are abelian""; ""Subgroups of fully residually free groups: algorithmic problems""; ""1. Introduction"" ""2. Preliminaries""""3. Intersection of two finitely generated subgroups of FZ[t]""; ""4. Properties of intersections of finitely generated subgroups of FZ[t]""; ""5. Centralizers in finitely generated fully residually free groups""; ""6. Conjugacy problem in finitely generated subgroups of FZ[t]""; ""References""; ""Weak hyperbolicity and free constructions""; ""Some properties of the conjugacy class growth function""; ""Boundary test elements""; ""Geodesics in the braid group on three strands""; ""Remarks on the growth of inverse semigroups"" ""Assessing security of some group based cryptosystems"" |
| Record Nr. | UNINA-9910788667803321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors
| Group theory, statistics, and cryptography : AMS Special Session, Combinatorial and Statistical Group Theory, April 12-13, 2003, New York University / / Alexei G. Myasnikov, Vladimir Shpilrain, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (186 p.) |
| Disciplina | 512/.2 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Group theory
Mathematical statistics Cryptography |
| ISBN | 0-8218-7950-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""On power- and commutation transitive, power commutative, and restricted Gromov groups""; ""Braid-based cryptography""; ""1. Background on braids""; ""1.1. Braid groups""; ""1.2. The greedy normal form""; ""1.3. Implementation of braids""; ""2. Braid-based schemes""; ""2.1. Key exchange""; ""2.2. Enciphering�deciphering""; ""2.3. Authentication""; ""2.4. Signature""; ""3. Attacks against the braid schemes""; ""3.1. Solutions to the Conjugacy Problem""; ""3.2. Attacks based on length""; ""3.3. Attacks based on linear representations""
""3.4. Are these attacks dangerous?""""4. Clues for further research""; ""4.1. Key generation""; ""4.2. Random drawing and security proofs""; ""4.3. Using braid words and braid reduction""; ""4.4. Hash functions""; ""4.5. Resorting to other braid problems""; ""5. Conclusion""; ""Discriminating and squarelike groups I: Axiomatics""; ""The density of small words in a free group is 0""; ""Braid groups and Aut(F2) are not rigid""; ""On varieties of groups in which all periodic groups are abelian""; ""Subgroups of fully residually free groups: algorithmic problems""; ""1. Introduction"" ""2. Preliminaries""""3. Intersection of two finitely generated subgroups of FZ[t]""; ""4. Properties of intersections of finitely generated subgroups of FZ[t]""; ""5. Centralizers in finitely generated fully residually free groups""; ""6. Conjugacy problem in finitely generated subgroups of FZ[t]""; ""References""; ""Weak hyperbolicity and free constructions""; ""Some properties of the conjugacy class growth function""; ""Boundary test elements""; ""Geodesics in the braid group on three strands""; ""Remarks on the growth of inverse semigroups"" ""Assessing security of some group based cryptosystems"" |
| Record Nr. | UNINA-9910817177003321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||