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math.GR2003
Genetic algorithms and the Andrews-Curtis conjecture
Alexei D. Miasnikov
The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be transformed into the trivial presentation by a finite sequence of "elementary tran…
math.GR2003
Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture
Alexei D. Miasnikov, Alexei G. Myasnikov
The Andrews-Curtis conjecture states that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of the elementary Nielsen transformation…
math.GR2003
Whitehead method and Genetic Algorithms
Alexei D. Miasnikov, Alexei G. Myasnikov
In this paper we discuss a genetic version (GWA) of the Whitehead's algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisi…