A GEOMETRIC ZERO-ONE LAW
ROBERT H. GILMAN, YURI GUREVICH, AND ALEXEI MIASNIKOV
Abstract. Each relational structure X has an associated Gaifman graph, which endows X with the properties of a graph. If x
is an element of X , let Bn (x) be the ball of radius
A CHARACTERISATION OF VIRTUALLY FREE GROUPS
ROBERT H. GILMAN, SUSAN HERMILLER, DEREK F. HOLT, AND SARAH REES
Abstract. We prove that a nitely generated group G is virtually free
if and only if there exists a generating set for G and k > 0 such that all
k-
New Developments in Commutator Key Exchange
Robert Gilman, Alex D. Miasnikov, Alexei G.
Myasnikov and Alexander Ushakov
Abstract. We study the algorithmic security of the Anshel-Anshel-Goldfeld
(AAG) key exchange scheme and show that contrary to prevalent
SOLVING ONE-VARIABLE EQUATIONS IN FREE GROUPS
DIMITRI BORMOTOV ROBERT GILMAN ALEXEI MYASNIKOV
Abstract. Equations in free groups have become prominent recently
in connection with the solution to the well known Tarski Conjecture.
Results of Makanin and Ras
Report on Generic Case Complexity
Robert Gilman
Alexei G. Miasnikov
Alexey D. Myasnikov
Alexander Ushakov
March 20, 2007
Abstract
This article is a short introduction to generic case complexity, which
is a recently developed way of measuring the diculty o
ON THE DEFINITION OF WORD HYPERBOLIC GROUPS
ROBERT H. GILMAN
Abstract. Formal languages based on multiplication tables of nitely
generated groups are investigated and used to give a linguistic characterization of word hyperbolic groups.
1. Introduction
Ov
Contemporary Mathematics
One Variable Equations in Free Groups
via Context Free Languages
Robert H. Gilman and Alexei G. Myasnikov
Abstract. We use context free languages to analyze solution sets to one variable equations over free groups.
Contents
1. Int
AUTOMATIC QUOTIENTS OF FREE GROUPS
ROBERT H. GILMAN
Abstract. Automatic groups admitting prex closed automatic
structures with uniqueness are characterized as the quotients of
free groups by normal subgroups possessing sets of free generators
satisfying c