Compressed Decision Problems in Hyperbolic Groups

Authors Derek Holt, Markus Lohrey, Saul Schleimer

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Derek Holt
  • University of Warwick, UK
Markus Lohrey
  • Universität Siegen, Germany
Saul Schleimer
  • University of Warwick, UK

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Derek Holt, Markus Lohrey, and Saul Schleimer. Compressed Decision Problems in Hyperbolic Groups. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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 words defined by straight-line programs defined over a finite generating set for the group. We prove also that, for any infinite hyperbolic group G, the compressed knapsack problem in G is NP-complete.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algebraic complexity theory
  • hyperbolic groups
  • algorithms for compressed words
  • circuit evaluation problems


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