2 citations · 2 across the 8 of their papers we have counts for
9 papers
Nonstandard free groups
Alexei Miasnikov, Andrey Nikolaev
Interpretation of a structure in allows to produce structures elementarily equivalent to given those elementarily equivalent to . In…
Quadratic equations in the Grigorchuk group
Igor Lysenok, Alexei Miasnikov, Alexander Ushakov
We provide an algorithm which, for a given quadratic equation in the Grigorchuk group determines if it has a solution. As a corollary to our approach, we prove that the group has a…
The Word Problem in the Baumslag group with a non-elementary Dehn function is polynomial time decidable
Alexei Miasnikov, Alexander Ushakov, Dong Wook Won
We prove that the Word problem in the Baumslag group G(1,2) which has a non-elementary Dehn function is decidable in polynomial time.
A Geometric Zero-One Law
Robert H. Gilman, Yuri Gurevich, Alexei Miasnikov
Each relational structure X has an associated Gaifman graph, which endows X with the properties of a graph. Suppose that X is infinite, connected and of bounded degree. A first-ord…
Pattern Recognition Approaches to Solving Combinatorial Problems in Free Groups
Robert M. Haralick, Alexei D. Miasnikov, Alexei G. Myasnikov
We review some basic methodologies from pattern recognition that can be applied to helping solve combinatorial problems in free group theory. We illustrate how this works with reco…
Heuristics for The Whitehead Minimization Problem
R. M. Haralick, A. D. Miasnikov, A. G. Myasnikov
In this paper we discuss several heuristic strategies which allow one to solve the Whitehead's minimization problem much faster (on most inputs) than the classical Whitehead algori…