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Complexity of Word Problems for HNN-Extensions

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Fundamentals of Computation Theory (FCT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12867))

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Abstract

The computational complexity of the word problem in HNN-extension 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 easily extended to fundamental groups of graphs of groups with hyperbolic vertex groups and cyclic edge groups.

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Notes

  1. 1.

    The concept of undistorted subgroups is defined for arbitrary finitely generated subgroups but we will need it only for the cyclic case.

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Acknowledgments

This work is supported by the DFG project LO748/12-1.

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  1. Universität Siegen, Siegen, Germany

    Markus Lohrey

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  1. Markus Lohrey
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Correspondence to Markus Lohrey .

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  1. Sorbonne University, Paris, France

    Evripidis Bampis

  2. National Technical University of Athens, Athens, Greece

    Aris Pagourtzis

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Lohrey, M. (2021). Complexity of Word Problems for HNN-Extensions. In: Bampis, E., Pagourtzis, A. (eds) Fundamentals of Computation Theory. FCT 2021. Lecture Notes in Computer Science(), vol 12867. Springer, Cham. https://doi.org/10.1007/978-3-030-86593-1_26

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  • DOI: https://doi.org/10.1007/978-3-030-86593-1_26

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