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Efficient Computation in Groups Via Compression

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Computer Science – Theory and Applications (CSR 2007)

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Abstract

We study the compressed word problem: a variant of the word problem for finitely generated groups where the input word is given by a context-free grammar that generates exactly one string. We show that finite extensions and free products preserve the complexity of the compressed word problem. Also, the compressed word problem for a graph group can be solved in polynomial time. These results allow us to obtain new upper complexity bounds for the word problem for certain automorphism groups and group extensions.

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Volker Diekert Mikhail V. Volkov Andrei Voronkov

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Lohrey, M., Schleimer, S. (2007). Efficient Computation in Groups Via Compression. In: Diekert, V., Volkov, M.V., Voronkov, A. (eds) Computer Science – Theory and Applications. CSR 2007. Lecture Notes in Computer Science, vol 4649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74510-5_26

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  • DOI: https://doi.org/10.1007/978-3-540-74510-5_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74509-9

  • Online ISBN: 978-3-540-74510-5

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