The bounded and precise word problems for presentations of groups:
We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise...
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
March 2020
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
volume 264, number 1281 (fourth of 6 numbers) |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, we obtain polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. We also obtain polynomial time bounds for these problems. |
| Beschreibung: | Literaturverzeichnis: Seite 105-106 |
| Beschreibung: | v, 106 Seiten Illustrationen |
| ISBN: | 9781470441432 |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 264, number 1281 (fourth of 6 numbers) | |
| 500 | |a Literaturverzeichnis: Seite 105-106 | ||
| 520 | |a We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, we obtain polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. We also obtain polynomial time bounds for these problems. | ||
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Datensatz im Suchindex
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| adam_text | American Mathematical Society
Number 1281
The Bounded and Precise Word
Problems for Presentations of
Groups
S V Ivanov
ULB Darmstadt
20396512
Universitäts- und
Landesbibliothek
Darmstadt
March 2020 • Volume 264 • Number 1281 (fourth of 6 numbers)
■ tit- American
A |v S mathematical
1 VI VLU SOCIETY
Contents
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Introduction
Preliminaries
Proof of Proposition 1 1
Calculus of Brackets for Group Presentation (1 2)
Proofs of Theorem 1 2 and Corollary 1 3
Calculus of Brackets for Group Presentation (1 4)
Proof of Theorem 1 4
Minimizing Diagrams over (1 2) and Proofs of Theorem 1 5 and
Corollary 1 6
Construction of Minimal Diagrams over (1 4) and Proof of
Theorem 1 7
Polygonal Curves in the Plane and Proofs of Theorems 1 8, 1 9
and Corollary 1 10
1
9
13
15
37
43
63
69
81
91
Bibliography
|
| adam_txt |
American Mathematical Society
Number 1281
The Bounded and Precise Word
Problems for Presentations of
Groups
S V Ivanov
ULB Darmstadt
20396512
Universitäts- und
Landesbibliothek
Darmstadt
March 2020 • Volume 264 • Number 1281 (fourth of 6 numbers)
■\ tit-' American
A |v\ S mathematical
1 VI VLU SOCIETY
Contents
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Introduction
Preliminaries
Proof of Proposition 1 1
Calculus of Brackets for Group Presentation (1 2)
Proofs of Theorem 1 2 and Corollary 1 3
Calculus of Brackets for Group Presentation (1 4)
Proof of Theorem 1 4
Minimizing Diagrams over (1 2) and Proofs of Theorem 1 5 and
Corollary 1 6
Construction of Minimal Diagrams over (1 4) and Proof of
Theorem 1 7
Polygonal Curves in the Plane and Proofs of Theorems 1 8, 1 9
and Corollary 1 10
1
9
13
15
37
43
63
69
81
91
Bibliography |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Ivanov, Sergei V. 1972- |
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| author_facet | Ivanov, Sergei V. 1972- |
| author_role | aut |
| author_sort | Ivanov, Sergei V. 1972- |
| author_variant | s v i sv svi |
| building | Verbundindex |
| bvnumber | BV046828568 |
| classification_rvk | SI 130 |
| ctrlnum | (OCoLC)1193159453 (DE-599)BVBBV046828568 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| isbn | 9781470441432 |
| language | English |
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| spelling | Ivanov, Sergei V. 1972- (DE-588)121330377X aut The bounded and precise word problems for presentations of groups S.V. Ivanov Providence, RI American Mathematical Society March 2020 v, 106 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 264, number 1281 (fourth of 6 numbers) Literaturverzeichnis: Seite 105-106 We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, we obtain polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. We also obtain polynomial time bounds for these problems. Geometrische Gruppentheorie (DE-588)4651615-3 gnd rswk-swf Geometrische Gruppentheorie (DE-588)4651615-3 s DE-604 Memoirs of the American Mathematical Society volume 264, number 1281 (fourth of 6 numbers) (DE-604)BV008000141 1281 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032237773&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivanov, Sergei V. 1972- The bounded and precise word problems for presentations of groups Memoirs of the American Mathematical Society Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| subject_GND | (DE-588)4651615-3 |
| title | The bounded and precise word problems for presentations of groups |
| title_auth | The bounded and precise word problems for presentations of groups |
| title_exact_search | The bounded and precise word problems for presentations of groups |
| title_exact_search_txtP | The bounded and precise word problems for presentations of groups |
| title_full | The bounded and precise word problems for presentations of groups S.V. Ivanov |
| title_fullStr | The bounded and precise word problems for presentations of groups S.V. Ivanov |
| title_full_unstemmed | The bounded and precise word problems for presentations of groups S.V. Ivanov |
| title_short | The bounded and precise word problems for presentations of groups |
| title_sort | the bounded and precise word problems for presentations of groups |
| topic | Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| topic_facet | Geometrische Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032237773&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT ivanovsergeiv theboundedandprecisewordproblemsforpresentationsofgroups |