CONTEXTFREE LANGUAGES OF
SUBEXPONENTIAL GROWTH
MARTIN R. BRIDSON AND ROBERT H. GILMAN
Abstract. There do not exist contextfree languages of intermediate growth.
The function whose value at each nonnegative integer n is the
number of words on length n in a
A SHRINKING LEMMA FOR INDEXED LANGUAGES
Robert H. Gilman
Abstract. This article presents a lemma in the spirit of the pumping lemma
for indexed languages but easier to employ.
Section 1. Introduction.
The pumping lemma for context-free languages has been
COMBING NILPOTENT AND POLYCYCLIC GROUPS
ROBERT H. GILMAN, DEREK F. HOLT, AND SARAH REES
Abstract. The notable exclusions from the family of automatic groups
are those nilpotent groups which are not virtually abelian, and the fundamental groups of compact
ON GROUPS WHOSE WORD PROBLEM IS SOLVED BY A
NESTED STACK AUTOMATON
ROBERT GILMAN AND MICHAEL SHAPIRO
Abstract. Accessible groups whose word problems are accepted by a
deterministic nested stack automaton with limited erasing are virtually
free.
1. Introdu
FORMAL LANGUAGES AND INFINITE GROUPS
ROBERT H. GILMAN
Abstract. This article is an introduction to formal languages
from the point of view of combinatorial group theory.
Contents
1. Introduction
2. Rational Sets
3. Rational Languages
4. Applications of Ra
FORMAL LANGUAGE THEORY AND
THE GEOMETRY OF 3-MANIFOLDS
Martin R. Bridson and Robert H. Gilman
Abstract.
Automatic groups were introduced in connection with geometric problems, in particular with the study of fundamental groups of 3-manifolds. In this
arti
A REMARK ABOUT COMBINGS OF GROUPS
Martin R. Bridson and Robert H. Gilman
Section 1. Introduction
In the last several years a remarkable interplay between geometry, group theory, and the theory of formal languages has led to developments including the
intr
THE GEOMETRY OF CYCLES IN THE
CAYLEY DIAGRAM OF A GROUP
Robert H. Gilman
Dedicated to the memory of Wilhelm Magnus
Abstract.
A study of triangulations of cycles in the Cayley diagrams of nitely
generated groups leads to a new geometric characterization of
Automatic Groups and String Rewriting
Robert H. Gilman
1
Introduction
In recent years developments in geometric topology have led to a remarkable
interplay between group theory, geometry, and the theory of automata and
formal languages. One of the best kn
ON BOUNDED LANGUAGES AND THE
GEOMETRY OF NILPOTENT GROUPS
Martin R. Bridson and Robert H. Gilman
Abstract.
Bounded languages are a class of formal languages which includes all
context free languages of polynomial growth. We prove that if a nitely generate