Add to ORKGWe prove that in a torsion-free hyperbolic group Γ, the length of the value of each variable in a minimal solution of a quadratic equation Q = 1 is bounded by N |Q|4 for an orientable equation, and by N |Q|16 for a non-orientable equation, where |Q | is the length of the equation, and the constant N can be computed. We show that the problem, whether a quadratic equation in Γ has a solution, is NP-complete, and that there is a PSpace algorithm for solving arbitrary equations in Γ. We also give a slightly larger bound for minimal solutions of quadratic equations in a toral relatively hyperbolic group.
We analyze the question of deciding whether a quadratic or a hyperbolic 0-1 programming instance has...
There is a quadratic-time algorithm that determines conjugacy between finite subsets in any torsion-...
The main result proved in this paper is that the conjugacy problem in word-hyperbolic groups is solv...
© Laura Ciobanu and Murray Elder; licensed under Creative Commons License CC-BY We show that the ful...
We show that the Diophantine problem, for quadratic equations over a non-elementary torsion-free hyp...
We show that the full set of solutions to systems of equations and inequations in a hyperbolic group...
It is a long standing conjecture that the problem of deciding whether a quadratic word equation has ...
In this thesis we consider two different types of algorithmic problems over groups. In the first par...
In [Se5] we proved that free and torsion-free hyperbolic groups are stable. In this note we give an ...
Prishchepov [16] proved that all equations of length at most six over torsion-free groups are solvab...
We show that for any finite-rank free group $\Gamma$, any word-equation in one variable of length $n...
We study conjugacy classes of solutions to systems of equations and inequations over torsion-free h...
If u and v are two conjugate elements of a hyperbolic group then the length of a shortest conjugatin...
The article discuses satisfiability of quadratic word equations. It reproduces results of Robson and...
We prove two theorems regarding the algorithmic theory of groups. First, that the compressed word pr...
We analyze the question of deciding whether a quadratic or a hyperbolic 0-1 programming instance has...
There is a quadratic-time algorithm that determines conjugacy between finite subsets in any torsion-...
The main result proved in this paper is that the conjugacy problem in word-hyperbolic groups is solv...
© Laura Ciobanu and Murray Elder; licensed under Creative Commons License CC-BY We show that the ful...
We show that the Diophantine problem, for quadratic equations over a non-elementary torsion-free hyp...
We show that the full set of solutions to systems of equations and inequations in a hyperbolic group...
It is a long standing conjecture that the problem of deciding whether a quadratic word equation has ...
In this thesis we consider two different types of algorithmic problems over groups. In the first par...
In [Se5] we proved that free and torsion-free hyperbolic groups are stable. In this note we give an ...
Prishchepov [16] proved that all equations of length at most six over torsion-free groups are solvab...
We show that for any finite-rank free group $\Gamma$, any word-equation in one variable of length $n...
We study conjugacy classes of solutions to systems of equations and inequations over torsion-free h...
If u and v are two conjugate elements of a hyperbolic group then the length of a shortest conjugatin...
The article discuses satisfiability of quadratic word equations. It reproduces results of Robson and...
We prove two theorems regarding the algorithmic theory of groups. First, that the compressed word pr...
We analyze the question of deciding whether a quadratic or a hyperbolic 0-1 programming instance has...
There is a quadratic-time algorithm that determines conjugacy between finite subsets in any torsion-...
The main result proved in this paper is that the conjugacy problem in word-hyperbolic groups is solv...