Complexity of Word Problems for HNN-Extensions

@inproceedings{Lohrey2021ComplexityOW,
  title={Complexity of Word Problems for HNN-Extensions},
  author={Markus Lohrey},
  booktitle={FCT},
  year={2021}
}
The computational complexity of the word problem in HNNextension of groups is studied. HNN-extension is a fundamental construction in combinatorial group theory. It is shown that the word problem for an ascending HNN-extension of a group H is logspace reducible to the so-called compressed word problem for H . The main result of the paper states that the word problem for an HNN-extension of a hyperbolic group H with cyclic associated subgroups can be solved in polynomial time. This result can be… Expand

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References

SHOWING 1-10 OF 39 REFERENCES
The Linearity of the Conjugacy Problem in Word-hyperbolic Groups
TLDR
It is proved that the conjugacy problem in word-hyperbolic groups is solvable in linear time using a standard RAM model of computation, in which basic arithmetical operations on integers are assumed to take place in constant time. Expand
The Nielsen Reduction and P-Complete Problems in Free Groups
TLDR
It is proved by encoding the computations of a deterministic polynomially time bounded TM into a subgroup of a free group and implementing the Nielsen reduction, one of the main tools for solving algorithmic problems in free groups, in polynomial time. Expand
Compressed Word Problems in HNN-extensions and Amalgamated Products
It is shown that the compressed word problem for an HNN-extension 〈H,t∣t−1at=ϕ(a) (a∈A)〉 with A finite is polynomial time Turing-reducible to the compressed word problem for the base group H. AnExpand
On the complexity of conjugacy in amalgamated products and HNN extensions
TLDR
This thesis deals with the conjugacy problem in classes of groups which can be written as HNN extension or amalgamated product, and shows that the comparison problem in power circuits is complete for P under logspace reductions and some basic transfer results for circuit complexity in the same class of groups. Expand
Word Problems Solvable in Logspace
TLDR
It is shown that the word problem for hnear groups (groups of matrices) over a field of characteristic 0 is solvable in (deterministic) logspace and hence the membership problem for the two-sided Dyck language are solable in logspace. Expand
Compressed Decision Problems in Hyperbolic Groups
We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as wordsExpand
Word processing in groups
TLDR
This study in combinatorial group theory introduces the concept of automatic groups and is of interest to mathematicians and computer scientists and includes open problems that will dominate the research for years to come. Expand
Logspace computations in graph products
We consider three important and well-studied algorithmic problems in group theory: the word, geodesic, and conjugacy problem. We show transfer results from individual groups to graph products. WeExpand
Verbal subgroups of hyperbolic groups have infinite width
TLDR
It is shown that the width of the verbal subgroup w(G) = 〈w[G]〉 is infinite and there is no such l ∈ Z that any g ∈ w (G) can be represented as a product of ≤ l values of w and their inverses. Expand
Context-Free Groups and Bass–Serre Theory
The word problem of a finitely generated group is the set of words over the generators that are equal to the identity in the group. The word problem is therefore a formal language. If this languageExpand
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