Algorithmic Problems in Groups, Semigroups and Inverse Semigroups

1995 ◽  
pp. 147-214 ◽  
Author(s):  
S. Margolis ◽  
J. Meakin ◽  
M. Sapir
Keyword(s):  
Inverse Semigroups ◽  
Algorithmic Problems

HNN Extensions of Inverse Semigroups and Applications

1997 ◽  
Vol 07 (05) ◽  
pp. 605-624 ◽  
Author(s):  
Akihiro Yamamura
Keyword(s):  
Inverse Semigroups ◽  
General Definition ◽  
Hnn Extensions ◽  
Hnn Extension ◽  
Algorithmic Problems ◽  
New Construction ◽  
Definition Of ◽  
Inverse Subsemigroups ◽  
Finitely Presented ◽  
Markov Properties

Originally the concept of an HNN extension of a group was introduced by Higman, Neumann and Neumann in their study of embeddability of groups. Howie introduced the concept of HNN extensions of semigroups and showed embeddability in the case that the associated subsemigroups are unitary. On the other hand, T. E. Hall showed the embeddability of HNN extensions of inverse semigroups of a special type in his survey article on amalgamation of inverse semigroups. We introduce a more general definition of an HNN extension and show that free inverse semigroups and the bicyclic semigroup are HNN extensions of semilattices as examples of our new construction. We discuss weak HNN embeddability in several classes of semigroups and strong HNN embeddability in the class of inverse semigroups. One of our main purposes in the study of HNN extensions of inverse semigroups is to employ HNN extensions to examine some algorithmic problems. We prove the undecidability of Markov properties of finitely presented inverse semigroups using HNN extensions. This result was announced by Vazhenin in 1978, but no proof of it has been published to date. We also show undecidability of several non-Markov properties and discuss some undecidable problems on finitely generated inverse subsemigroups of finitely presented inverse semigroups.

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.

scholarly journals Inverse semigroups with idempotent-fixing automorphisms

2014 ◽  
Vol 89 (2) ◽  
pp. 469-474 ◽  
Author(s):  
João Araújo ◽  
Michael Kinyon
Keyword(s):  
Inverse Semigroups

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.

On certain codes admitting inverse semigroups as syntactic monoids

1974 ◽  
Vol 8 (1) ◽  
pp. 312-331 ◽  
Author(s):  
Michael Keenan ◽  
Gerard Lallement
Keyword(s):  
Inverse Semigroups
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