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Musings on generic-case complexity

  • Ilya Kapovich
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Elementary Theory of Groups and Group Rings, and Related Topics
This chapter is in the book Elementary Theory of Groups and Group Rings, and Related Topics

Abstract

We propose a more general definition of generic-case complexity, based on using a random process for generating inputs of an algorithm and using the time needed to generate an input as a way of measuring the size of that input.

Abstract

We propose a more general definition of generic-case complexity, based on using a random process for generating inputs of an algorithm and using the time needed to generate an input as a way of measuring the size of that input.

Chapters in this book

  1. Frontmatter I
  2. Introduction V
  3. Conference booklet and talks VII
  4. Remembrances of Gilbert XI
  5. Contents XXIX
  6. Explicit universal axioms for Kaplansky groups 1
  7. Isoperimetric and isodiametric functions of group extensions 7
  8. The homology of groups, profinite completions, and echoes of Gilbert Baumslag 11
  9. Some properties of the Baumslag groups G(m, n) 29
  10. Some model theory of the Heisenberg group: I. Unitriangular representations of models of a subtheory of its universal theory 33
  11. Some model theory of the Heisenberg group: II. The three generator case 47
  12. On vector-valued Hecke forms 53
  13. Two algorithms in group theory 73
  14. On products of closed subsets in free groups 81
  15. Misbehaved direct products 85
  16. A survey on Albert algebras and groups of type F4 89
  17. Perspectives on p-ary bent functions 103
  18. Multilinear cryptography using nilpotent groups 127
  19. Musings on generic-case complexity 135
  20. Noncommutative Gebauer–Möller criteria 149
  21. On the numbers of the form x2 + 11y2 177
  22. Separability properties of nilpotent ℚ[x]-powered groups 203
  23. Infinite nested radicals 219
  24. Commutative transitivity property in groups and Lie algebras 225
  25. Simplicial subdivisions and the chromatic number of a group 233
https://doi.org/10.1515/9783110638387-014

Chapters in this book

  1. Frontmatter I
  2. Introduction V
  3. Conference booklet and talks VII
  4. Remembrances of Gilbert XI
  5. Contents XXIX
  6. Explicit universal axioms for Kaplansky groups 1
  7. Isoperimetric and isodiametric functions of group extensions 7
  8. The homology of groups, profinite completions, and echoes of Gilbert Baumslag 11
  9. Some properties of the Baumslag groups G(m, n) 29
  10. Some model theory of the Heisenberg group: I. Unitriangular representations of models of a subtheory of its universal theory 33
  11. Some model theory of the Heisenberg group: II. The three generator case 47
  12. On vector-valued Hecke forms 53
  13. Two algorithms in group theory 73
  14. On products of closed subsets in free groups 81
  15. Misbehaved direct products 85
  16. A survey on Albert algebras and groups of type F4 89
  17. Perspectives on p-ary bent functions 103
  18. Multilinear cryptography using nilpotent groups 127
  19. Musings on generic-case complexity 135
  20. Noncommutative Gebauer–Möller criteria 149
  21. On the numbers of the form x2 + 11y2 177
  22. Separability properties of nilpotent ℚ[x]-powered groups 203
  23. Infinite nested radicals 219
  24. Commutative transitivity property in groups and Lie algebras 225
  25. Simplicial subdivisions and the chromatic number of a group 233
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