Log-space conjugacy problem in the Grigorchuk group

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Alexei Miasnikov ◽  
Svetla Vassileva
Keyword(s):  
Conjugacy Problem ◽  
Space Complexity ◽  
Grigorchuk Group

AbstractIn this paper we prove that the conjugacy problem in the Grigorchuk group Γ has log-space complexity.

Log-Space Complexity of the Conjugacy Problem in Wreath Products

2017 ◽  
pp. 215-236 ◽  
Author(s):  
Alexei Myasnikov ◽  
Svetla Vassileva ◽  
Armin Weiss
Keyword(s):  
Conjugacy Problem ◽  
Wreath Products ◽  
Space Complexity

scholarly journals Linear time algorithm for the conjugacy problem in the first Grigorchuk group

2021 ◽  
pp. 1-18
Author(s):  
Mitra Modi ◽  
Mathew Seedhom ◽  
Alexander Ushakov
Keyword(s):  
Polynomial Time ◽  
Linear Time ◽  
Conjugacy Problem ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Conjugate Element ◽  
Grigorchuk Group

We prove that the conjugacy problem in the first Grigorchuk group [Formula: see text] can be solved in linear time. Furthermore, the problem to decide if a list of elements [Formula: see text] contains a pair of conjugate elements can be solved in linear time. We also show that a conjugator for a pair of conjugate element [Formula: see text] can be found in polynomial time.

scholarly journals The conjugacy problem in the Grigorchuk group is polynomial time decidable

2010 ◽  
pp. 813-833 ◽  
Author(s):  
Igor Lysenok ◽  
Alexei Myasnikov ◽  
Alexander Ushakov
Keyword(s):  
Polynomial Time ◽  
Conjugacy Problem ◽  
Grigorchuk Group

On the closure of the first Grigorchuk group

2011 ◽  
Vol 173 (4) ◽  
pp. 371-377
Author(s):  
Yuriy G. Leonov
Keyword(s):  
Grigorchuk Group

scholarly journals Conjugacy Problem in the Fundamental Groups of High-Dimensional Graph Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1330
Author(s):  
Raeyong Kim
Keyword(s):  
Group Structure ◽  
Conjugacy Problem ◽  
High Dimensional ◽  
Fundamental Groups ◽  
Graph Manifold ◽  
Solvable Word Problem ◽  
Algorithmic Problems ◽  
Graph Manifolds ◽  
Dimensional Graph ◽  
Solvable Word

The conjugacy problem for a group G is one of the important algorithmic problems deciding whether or not two elements in G are conjugate to each other. In this paper, we analyze the graph of group structure for the fundamental group of a high-dimensional graph manifold and study the conjugacy problem. We also provide a new proof for the solvable word problem.

Research on Asset Recognition Algorithm of Information Security Product Based on Decision Tree Algorithm

2013 ◽  
Vol 397-400 ◽  
pp. 2296-2300 ◽  
Author(s):  
Fei Shuai ◽  
Jun Quan Li
Keyword(s):  
Computational Complexity ◽  
Information Security ◽  
Decision Tree ◽  
Recognition Algorithm ◽  
Space Complexity ◽  
Complex Relationship ◽  
Decision Tree Algorithm ◽  
Tree Algorithm ◽  
C4.5 Algorithm ◽  
C4.5 Decision Tree

In current, there are complex relationship between the assets of information security product. According to this characteristic, we propose a new asset recognition algorithm (ART) on the improvement of the C4.5 decision tree algorithm, and analyze the computational complexity and space complexity of the proposed algorithm. Finally, we demonstrate that our algorithm is more precise than C4.5 algorithm in asset recognition by an application example whose result verifies the availability of our algorithm.Keywordsdecision tree, information security product, asset recognition, C4.5

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