Groups with Context‐Free Co‐Word Problem

@article{Holt2005GroupsWC,
  title={Groups with Context‐Free Co‐Word Problem},
  author={Derek F. Holt and Sarah Rees and Claas E. R{\"o}ver and Richard M. Thomas},
  journal={Journal of the London Mathematical Society},
  year={2005},
  volume={71}
}
  • D. HoltSarah Rees R. Thomas
  • Published 1 June 2005
  • Mathematics, Computer Science
  • Journal of the London Mathematical Society
The class of co‐context‐free groups is studied. A co‐context‐free group is defined as one whose co‐word problem (the complement of its word problem) is context‐free. This class is larger than the subclass of context‐free groups, being closed under the taking of finite direct products, restricted standard wreath products with context‐free top groups, and passing to finitely generated subgroups and finite index overgroups. No other examples of co‐context‐free groups are known. It is proved that… 
View on Wiley
wrap.warwick.ac.uk
58 Citations
Highly Influential Citations
8
Background Citations
30
Methods Citations
5
Results Citations
2

58 Citations

The co‐word problem for the Higman‐Thompson group is context‐free

The co‐word problem of a group G generated by a set X is defined as the set of words in X which do not represent 1 in G. We introduce a new method to show that a permutation group has context‐free…

LOCAL SIMILARITY GROUPS WITH CONTEXT-FREE CO-WORD PROBLEM

Let G be a group, and let S be a finite subset of G that generates G as a monoid. The co-word problem is the collection of words in the free monoid S ∗ that represent non-trivial elements of G. A…

Groups with poly-context-free word problem

It is shown that any group which is virtually a finitely generated subgroup of a direct product of free groups has poly-context-free word problem, and conjecture that the converse also holds is proved.

Groups with Indexed Co-word Problem

It is shown that all Higman–Thompson groups and a large class of tree automorphism groups defined by finite automata are co-indexed groups, including the Grigorchuk 2-group and the Gupta–Sidki 3-group.

Context-Freeness of Higman-Thompson group's co-word problem

AbstractThe co-word problem of a group G generated by a set X is defined asthe set of words in X which do not represent 1 in G. We introduce a newmethod to decide if a permutation group has…

Non-finitely Generated Maximal Subgroups of Context-free Monoids

Word Problem Languages for Free Inverse Monoids

It is shown that no free inverse monoid has context-free word problem, and that the word problem of the free inversemonoid of rank $1$ is both $2$-context-free (an intersection of two context- free languages) and ET0L.

Semigroups with a Context-Free Word Problem

The depth of the Muller-Schupp result and its reliance on the geometrical structure of Cayley graphs of groups suggests that a generalization to semigroups could be very hard to obtain, but some results are able to prove about this intriguing class of semig groups.

Church-Rosser Groups and Growing Context-Sensitive Groups

The free abelian group of rank 2 is a non-context-free Church-Rosser group, and it is shown that there are co- context-free groups that are not growing context-sensitive.

Context-free word problem semigroups

Some examples are exhibited to clarify the relationship between semigoups and monoids and their connection with the notions of word-hyperbolicity and automaticity and whether these classes are closed under applying certain semigroup constructions, including direct products and free products.
...

References

SHOWING 1-10 OF 20 REFERENCES

Groups with Indexed Co-word Problem

It is shown that all Higman–Thompson groups and a large class of tree automorphism groups defined by finite automata are co-indexed groups, including the Grigorchuk 2-group and the Gupta–Sidki 3-group.

Groups, the Theory of Ends, and Context-Free Languages

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

On a subclass of context-free groups

  • T. Herbst
  • Mathematics, Computer Science
    RAIRO Theor. Informatics Appl.
  • 1991
Plusieurs caracterisations de cette classe forment la classe la plus importante entre les groupes context-free et les groupe finis.

On Group-Theoretic Decision Problems and Their Classification.

Part exposition and part presentation of new results, this monograph deals with that area of mathematics which has both combinatorial group theory and mathematical logic in common. Its main topics…

A Course in the Theory of Groups

This is a detailed introduction to the theory of groups: finite and infinite; commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the…

Introduction to Automata Theory, Languages and Computation

The Language of Machines: an Introduction to Computability and Formal Languages

An up-to-date, authoritative text for courses in theory of computability and languages. The authors redefine the building blocks of automata theory by offering a single unified model encompassing all…

Algebraic Number Theory

I: Algebraic Integers.- II: The Theory of Valuations.- III: Riemann-Roch Theory.- IV: Abstract Class Field Theory.- V: Local Class Field Theory.- VI: Global Class Field Theory.- VII: Zeta Functions…

Combinatorial Group Theory

These notes were prepared for use by the participants in the Workshop on Algebra, Geometry and Topology held at the Australian National University, 22 January to 9 February, 1996. They have…