## 244 Citations

### Automatic Groups and String Rewriting

- MathematicsTerm Rewriting
- 1993

This article considers automatic groups from the point of view of automata and language theory, and sees how work of Epstein, Holt and Rees puts automatic groups naturally into the context of string rewriting.

### Descriptions of groups using formal language theory

- Mathematics, Computer Science
- 2016

The main contribution is the fact that a group for which all irreducible word problems are recursively enumerable must necessarily have solvable word problem.

### The Theory of Ends, Pushdown Automata, and Second-Order Logic

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1985

### Groups and simple languages

- Mathematics
- 1983

With any finitely generated group presentation, one can associate a formal language (called the reduced word problem) consisting of those words on the generators and their inverses which are equal toâ€¦

### Groups, formal language theory and decidability

- Mathematics
- 2015

The first four chapters provide an introduction, background information and a summary of results from some of the relevant literature, and some characterisations of monoids based on properties that the full preimage of certain subsets satisfy when considered as a formal language over the generating set are proved.

### Context-Free Languages

- Computer ScienceHandbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
- 1990

### Extended Finite Automata and Word Problems

- Mathematics, Computer ScienceInt. J. Algebra Comput.
- 2005

It is shown that the family of languages accepted by extended finite automata over a monoid K is controlled by the word problem of K in a precisely stated manner and it is deduced that along with the free group of rank two, the only finitely generated groups with this property are precisely the groups that have a nonabelian free subgroup of finite index.

### Formal Languages and the Word Problem for Groups

- Mathematics
- 2013

The aim of this article is to survey some connections between formal language theory and group theory with particular emphasis on the word problem for groups and the consequence on the algebraicâ€¦

### Decidable Theories of Cayley-Graphs

- MathematicsSTACS
- 2003

It is proved that a connected graph of bounded degree with only finitely many orbits has a decidable MSO-theory if and only if it is context-free, and a new unfolding construction is introduced, the factorized unfolding, that generalizes the tree-like structures considered by Walukiewicz.

### On a class of poly-context-free groups generated by automata

- Mathematics
- 2022

. This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize theâ€¦

## References

SHOWING 1-10 OF 12 REFERENCES

### Pushdown automata, graphs, ends, second-order logic, and reachability problems

- Computer Science, MathematicsSTOC '81
- 1981

It is shown that the monadic second-order theory of any context-free graph is decidable, and using the results obtained and Rabin's theorem, this work shows that cellular automata and vector addition systems make sense on a very general class of graphs.

### Groups and simple languages

- Mathematics
- 1983

With any finitely generated group presentation, one can associate a formal language (called the reduced word problem) consisting of those words on the generators and their inverses which are equal toâ€¦

### Groups of Cohomological Dimension One

- Mathematics
- 1972

Cohomology theory.- Ends.- The structure theorem.- The augmentation ideal.- The finitely generated case.- The countable case.- Splitting theorems.- The main theorems.

### Finite and infinite cyclic extensions of free groups

- MathematicsJournal of the Australian Mathematical Society
- 1973

Using Stalling's characterization [11] of finitely generated (f. g.) groups with infinitely many ends, and subgroup theorems for generalized free products and HNN groups (see [9], [5], and [7]), weâ€¦

### Connection between context-free groups and groups with decidable problems of automata equivalence

- Mathematics
- 1976

### Introduction to formal language theory

- Computer Science
- 1978

The theory of formal languages has been developed extensively, and has several discernible trends, which include applications to the syntactic analysis of programming languages, program schemes, models of biological systems, and relationships with natural languages.