Random van Kampen diagrams and algorithmic problems in groups

2011 ◽  
Vol 3 (1) ◽  
Author(s):  
Alexei Myasnikov ◽  
Alexander Ushakov
Keyword(s):  
Van Kampen Diagrams ◽  
Algorithmic Problems

On generic complexity of the subset sum problem in monoids and groups of integer matrix of order two

2020 ◽  
Vol 25 (4) ◽  
pp. 10-15
Author(s):  
Alexander Nikolaevich Rybalov
Keyword(s):  
Linear Group ◽  
Modular Group ◽  
Special Linear Group ◽  
Second Order ◽  
Integer Matrix ◽  
Subset Sum ◽  
Algorithmic Problems ◽  
Almost All ◽  
Subset Sum Problems ◽  
Generic Complexity

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.

Allowed Boundary Sequences for Fused Polycyclic Patches and Related Algorithmic Problems

2001 ◽  
Vol 41 (2) ◽  
pp. 300-308 ◽  
Author(s):  
Michel Deza ◽  
Patrick W. Fowler ◽  
Viatcheslav Grishukhin
Keyword(s):  
Algorithmic Problems

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.

Some algorithmic problems of plotting codes for unstructured grids

1989 ◽  
Author(s):  
RAINALD LOEHNER ◽  
PARESH PARIKH ◽  
CLYDE GUMBERT
Keyword(s):  
Unstructured Grids ◽  
Algorithmic Problems

Aqueous Solutions of Algorithmic Problems: Emphasizing Knights on a 3 × 3

2002 ◽  
pp. 191-202 ◽  
Author(s):  
Tom Head ◽  
Xia Chen ◽  
Matthew J. Nichols ◽  
Masayuki Yamamura ◽  
Susannah Gal
Keyword(s):  
Aqueous Solutions ◽  
Algorithmic Problems

scholarly journals THE SUBWORD REVERSING METHOD

2011 ◽  
Vol 21 (01n02) ◽  
pp. 71-118 ◽  
Author(s):  
PATRICK DEHORNOY
Keyword(s):  
Word Problem ◽  
Semigroup Theory ◽  
Efficient Solutions ◽  
Preferred Direction ◽  
Van Kampen Diagrams ◽  
Left And Right

We summarize the main known results involving subword reversing, a method of semigroup theory for constructing van Kampen diagrams by referring to a preferred direction. In good cases, the method provides a powerful tool for investigating presented (semi)groups. In particular, it leads to cancellativity and embeddability criteria for monoids and to efficient solutions for the word problem of monoids and groups of fractions. The text includes some new results about mixed reversing (combination of left- and right-reversings) and about the combinatorial distance of braids.

Sign in / Sign up

Export Citation Format

Share Document