• Corpus ID: 244130409

Evaluation problems for the Thompson group and the Brin-Thompson group, and their relation to the word problem

@article{Birget2021EvaluationPF,
  title={Evaluation problems for the Thompson group and the Brin-Thompson group, and their relation to the word problem},
  author={Jean-Camille Birget},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.08646}
}
  • J. Birget
  • Published 16 November 2021
  • Mathematics
  • ArXiv
The Thompson group V , as well as the Brin-Thompson group 2V , is finitely generated and can be defined as a monoid acting on bitstrings, respectively pairs of bitstrings. Therefore evaluation problems can be defined for V and 2V . We show that these evaluation problems reduce to the corresponding word problems, and that in general, these evaluation problems are actually equivalent to the word problems. The long-input version of the evaluation problem is deterministic context-free and reverse… 

References

SHOWING 1-10 OF 20 REFERENCES

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

The Groups of Richard Thompson and Complexity

  • J. Birget
  • Mathematics
    Int. J. Algebra Comput.
  • 2004
TLDR
It is shown that V contains all finite direct products of finitely generated free groups as subgroups with linear distortion, and that up to polynomial equivalence of functions, the following three sets are the same: the set of distortions of V, theSet of Dehn functions offinitely presented groups, and theset of time complexity functions of nondeterministic Turing machines.

Circuits, coNP-completeness, and the groups of Richard Thompson

We construct a finitely presented group with coNP-complete word problem, and a finitely generated simple group with coNP-complete word problem. These groups are represented as Thompson groups, hence

A monoid version of the Brin-Higman-Thompson groups

We generalize the Brin-Higman-Thompson groups $n G_{k,1}$ to monoids $n M_{k,1}$, for $n \ge 1$ and $k \ge 2$, by replacing bijections by partial functions. The monoid $n M_{k,1}$ has $n G_{k,1}$ as

The infinite simple group V of Richard J. Thompson : presentations by permutations

We show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group $V$, known by Thompson to have a presentation with four generators and fourteen relations,

An Introduction to Formal Language Theory

TLDR
This volume intended to serve as a text for upper undergraduate and graduate level students and special emphasis is given to the role of algebraic techniques in formal language theory through a chapter devoted to the fixed point approach to the analysis of context-free languages.

The complexity of theorem-proving procedures

  • S. Cook
  • Mathematics, Computer Science
    STOC
  • 1971
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a