scholarly journals Knapsack and subset sum problems in nilpotent, polycyclic, and co-context-free groups

2016 ◽  
pp. 129-144 ◽  
Author(s):  
Daniel König ◽  
Markus Lohrey ◽  
Georg Zetzsche
Keyword(s):  
Free Groups ◽  
Subset Sum ◽  
Subset Sum Problems ◽  
Context Free

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 Network Structure of a System coded by Groups

1980 ◽  
Vol 35 (5) ◽  
pp. 526-530
Author(s):  
H. G. Busse ◽  
B. H. Havsteen
Keyword(s):  
Kinetic Model ◽  
Network Structure ◽  
Biological Systems ◽  
Free Groups ◽  
Chemical Kinetic ◽  
Mathematical Tool ◽  
Systematic Treatment ◽  
Chemical Kinetic Model ◽  
Linear Sequence ◽  
Context Free

Abstract A system may be characterized by its dynamics as well as by its structure. Several kinds of schematic drawings have been proposed to represent the structure of a system. Here, the representation of the structure by free groups is discussed. Free groups are an abstract mathematical tool, which permits the systematic treatment of a structure. The suggestion is exemplified by its application to a chemical kinetic model. The structure of the model is given (coded) by a linear sequence of symbols. The interaction of the environment with the structure (mutation) and the relation between structure and systemic boundaries (finiteness) are treated. The concept probably also applies to biological systems. Also, context-free languages could be used as alternate representations of system structures.

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