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Streaming in Graph Products

Authors Markus Lohrey , Julio Xochitemol

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Author Details

Markus Lohrey
  • Universität Siegen, Germany
Julio Xochitemol
  • Universität Siegen, Germany

Funding

  • Xochitemol, Julio: Funded by DFG project LO 748/13-2.

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Markus Lohrey and Julio Xochitemol. Streaming in Graph Products. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 71:1-71:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.71

Abstract

We investigate the streaming space complexity of word problems for groups. Using so-called distinguishers, we prove a transfer theorem for graph products of groups. Moreover, we use distinguishers to obtain a logspace streaming algorithm for the membership problem in a finitely generated subgroup of a free group.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • word problems for groups
  • streaming algorithms
  • graph products

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References

  1. Ajesh Babu, Nutan Limaye, Jaikumar Radhakrishnan, and Girish Varma. Streaming algorithms for language recognition problems. Theoretical Computer Science, 494:13-23, 2013. URL: https://doi.org/10.1016/j.tcs.2012.12.028.
  2. Gabriel Bathie and Tatiana Starikovskaya. Property testing of regular languages with applications to streaming property testing of visibly pushdown languages. In Proceedings of the 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, volume 198 of LIPIcs, pages 119:1-119:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.119.
  3. J. Berstel. Transductions and context-free languages. Teubner Studienbücher, Stuttgart, 1979. URL: https://doi.org/10.1007/978-3-663-09367-1.
  4. William W. Boone. The word problem. Annals of Mathematics. Second Series, 70:207-265, 1959. URL: https://doi.org/10.2307/1970103.
  5. Max Dehn. Über unendliche diskontinuierliche Gruppen. Mathematische Annalen, 71:116-144, 1911. In German. URL: https://doi.org/10.1007/BF01456932.
  6. Volker Diekert and Jonathan Kausch. Logspace computations in graph products. Journal of Symbolic Computation, 75:94-109, 2016. URL: https://doi.org/10.1016/j.jsc.2015.11.009.
  7. Nathanaël François, Frédéric Magniez, Michel de Rougemont, and Olivier Serre. Streaming property testing of visibly pushdown languages. In Proceedings of the 24th Annual European Symposium on Algorithms, ESA 2016, volume 57 of LIPIcs, pages 43:1-43:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. URL: https://doi.org/10.4230/LIPIcs.ESA.2016.43.
  8. Elisabeth R. Green. Graph Products of Groups. PhD thesis, The University of Leeds, 1990. Google Scholar
  9. Derek F. Holt, Sarah Rees, and Claas E. Röver. Groups, Languages and Automata, volume 88 of London Mathematical Society Student Texts. Cambridge University Press, 2017. URL: https://doi.org/10.1017/9781316588246.
  10. Tim Hsu and Daniel T. Wise. On linear and residual properties of graph products. Michigan Mathematical Journal, 46(2):251-259, 1999. URL: https://doi.org/10.1307/mmj/1030132408.
  11. Stephen P. Humphries. On representations of Artin groups and the Tits conjecture. Journal of Algebra, 169(3):847-862, 1994. URL: https://doi.org/10.1006/jabr.1994.1312.
  12. Ilya Kapovich and Alexei Myasnikov. Stallings foldings and subgroups of free groups. Journal of Algebra, 248(2):608-668, 2002. URL: https://doi.org/10.1006/jabr.2001.9033.
  13. Jonathan Kausch. The parallel complexity of certain algorithmic problems in group theory. PhD thesis, University of Stuttgart, 2017. URL: 10.18419/opus-9152.
  14. Markus Lohrey. Decidability and complexity in automatic monoids. International Journal of Foundations of Computer Science, 16(4):707-722, 2005. URL: https://doi.org/10.1142/S0129054105003248.
  15. Markus Lohrey. The Compressed Word Problem for Groups. SpringerBriefs in Mathematics. Springer, 2014. URL: https://doi.org/10.1007/978-1-4939-0748-9.
  16. Markus Lohrey and Lukas Lück. Streaming word problems. In Proceedings of the 47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022, volume 241 of LIPIcs, pages 72:1-72:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPICS.MFCS.2022.72.
  17. Markus Lohrey, Lukas Lück, and Julio Xochitemol. Streaming word problems. CoRR, abs/2202.04060, 2022. URL: https://arxiv.org/abs/2202.04060.
  18. Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. Recognizing well-parenthesized expressions in the streaming model. SIAM Journal on Computing, 43(6):1880-1905, 2014. URL: https://doi.org/10.1137/130926122.
  19. K. A. Mihaĭlova. The occurrence problem for direct products of groups. Math. USSR Sbornik, 70:241-251, 1966. English translation. Google Scholar
  20. Pjotr S. Novikov. On the algorithmic unsolvability of the word problem in group theory. American Mathematical Society, Translations, II. Series, 9:1-122, 1958. URL: https://doi.org/10.1090/trans2/009.
  21. Azaria Paz. Introduction to Probabilistic Automata. Academic Press, 1971. URL: https://doi.org/10.1016/C2013-0-11297-4.
  22. Michael O. Rabin. Probabilistic automata. Information and Control, 6(3):230-245, 1963. URL: https://doi.org/10.1016/S0019-9958(63)90290-0.
  23. B. A. F. Wehrfritz. Wreath products and chief factors of linear groups. Journal of the London Mathematical Society (2), 4:671-681, 1972. URL: https://doi.org/10.1112/jlms/s2-4.4.671.
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