Document Open Access Logo

Brief Announcement: Solvability of Three-Process General Tasks

Authors Hagit Attiya , Pierre Fraigniaud , Ami Paz , Sergio Rajsbaum

PDF

File

Thumbnail PDF
PDF
LIPIcs.DISC.2024.42.pdf
  • Filesize: 1.13 MB
  • 7 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Wait-free computing
  • lower bounds
  • topology

Metrics

Abstract

The topological view on distributed computing represents a task T as a relation Δ between the complex ℐ of its inputs and the complex 𝒪 of its outputs. A cornerstone result in the field is an elegant computability characterization of the solvability of colorless tasks in terms of ℐ, 𝒪 and Δ. Essentially, a colorless task is wait-free solvable if and only if there is a continuous map from the geometric realization of ℐ to that of 𝒪 that respects Δ.
This paper makes headway towards providing an analogous characterization for general tasks, which are not necessarily colorless, by concentrating on the case of three-process inputless tasks. Our key contribution is identifying local articulation points as an obstacle for the solvability of general tasks, and defining a topological deformation on the output complex of a task T, which eliminates these points by splitting them, to obtain a new task T', with an adjusted relation Δ' between the input complex ℐ and an output complex 𝒪' without articulation points. We obtain a new characterization of wait-free solvability of three-process general tasks: T is wait-free solvable if and only if there is a continuous map from the geometric realization of ℐ to that of 𝒪' that respects Δ'.

Cite As Get BibTex

Hagit Attiya, Pierre Fraigniaud, Ami Paz, and Sergio Rajsbaum. Brief Announcement: Solvability of Three-Process General Tasks. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 42:1-42:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.42

Author Details

Hagit Attiya
  • Department of Computer Science, Technion, Haifa, Israel
Pierre Fraigniaud
  • IRIF - CNRS & Université Paris Cité, France
Ami Paz
  • LISN - CNRS & Université Paris-Saclay, France
Sergio Rajsbaum
  • Instituto de Matemáticas, UNAM, Mexico City, Mexico

Funding

  • Attiya, Hagit: partially supported by the Israel Science Foundation (22/1425).
  • Fraigniaud, Pierre: partially supported by the ANR projects DUCAT (ANR-20-CE48-0006), FREDDA (ANR-17-CE40-0013), and QuData (ANR-18-CE47-0010).
  • Rajsbaum, Sergio: Partially done while visiting IRIF-France and supported by the ANR project DUCAT (ANR-20-CE48-0006).

References

  1. Luis Alberto. Pseudospheres: combinatorics, topology and distributed systems. Journal of Applied and Computational Topology, 2024. URL: https://doi.org/10.1007/s41468-023-00162-5.
  2. Dan Alistarh, James Aspnes, Faith Ellen, Rati Gelashvili, and Leqi Zhu. Why extension-based proofs fail. SIAM Journal on Computing, 52(4):913-944, 2023. URL: https://doi.org/10.1137/20M1375851.
  3. Hagit Attiya, Amotz Bar-Noy, Danny Dolev, David Peleg, and Rüdiger Reischuk. Renaming in an asynchronous environment. J. ACM, 37(3):524-548, 1990. URL: https://doi.org/10.1145/79147.79158.
  4. Hagit Attiya, Armando Castañeda, and Sergio Rajsbaum. Locally solvable tasks and the limitations of valency arguments. In 24th International Conference on Principles of Distributed Systems (OPODIS), volume 184, pages 18:1-18:16, 2020. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2020.18.
  5. Ofer Biran, Shlomo Moran, and Shmuel Zaks. A combinatorial characterization of the distributed 1-solvable tasks. Journal of algorithms, 11(3):420-440, 1990. URL: https://doi.org/10.1016/0196-6774(90)90020-F.
  6. Dobrina Boltcheva, David Canino, Sara Merino Aceituno, Jean-Claude Léon, Leila De Floriani, and Franck Hétroy. An iterative algorithm for homology computation on simplicial shapes. Computer-Aided Design, 43(11):1457-1467, 2011. Solid and Physical Modeling 2011. URL: https://doi.org/10.1016/j.cad.2011.08.015.
  7. Elizabeth Borowsky, Eli Gafni, Nancy A. Lynch, and Sergio Rajsbaum. The BG distributed simulation algorithm. Distributed Comput., 14(3):127-146, 2001. URL: https://doi.org/10.1007/PL00008933.
  8. Soma Chaudhuri. More choices allow more faults: Set consensus problems in totally asynchronous systems. Inf. Comput., 105(1):132-158, 1993. URL: https://doi.org/10.1006/INCO.1993.1043.
  9. Leila De Floriani, Mostefa M. Mesmoudi, Franco Morando, and Enrico Puppo. Decomposing non-manifold objects in arbitrary dimensions. Graphical Models, 65(1):2-22, 2003. URL: https://doi.org/10.1016/S1524-0703(03)00006-7.
  10. Michael J. Fischer, Nancy A. Lynch, and Mike Paterson. Impossibility of distributed consensus with one faulty process. J. ACM, 32(2):374-382, 1985. URL: https://doi.org/10.1145/3149.214121.
  11. Eli Gafni and Elias Koutsoupias. Three-processor tasks are undecidable. SIAM Journal on Computing, 28(3):970-983, 1998. URL: https://doi.org/10.1137/S0097539796305766.
  12. Hugo Rincon Galeana, Sergio Rajsbaum, and Ulrich Schmid. Continuous tasks and the asynchronous computability theorem. In 13th Innovations in Theoretical Computer Science Conference, ITCS, pages 73:1-73:27, 2022. URL: https://doi.org/10.4230/LIPICS.ITCS.2022.73.
  13. John Havlicek. Computable obstructions to wait-free computability. Distributed Computing, 13(2):59-83, 2000. URL: https://doi.org/10.1007/s004460050068.
  14. Maurice Herlihy, Dmitry N. Kozlov, and Sergio Rajsbaum. Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, 2013. Google Scholar
  15. Maurice Herlihy and Sergio Rajsbaum. The decidability of distributed decision tasks. In Proceedings of the 29th annual ACM symposium on Theory of computing, pages 589-598, 1997. Google Scholar
  16. Maurice Herlihy and Sergio Rajsbaum. A classification of wait-free loop agreement tasks. Theoretical Computer Science, 291(1):55-77, 2003. URL: https://doi.org/10.1016/S0304-3975(01)00396-6.
  17. Maurice Herlihy, Sergio Rajsbaum, Michel Raynal, and Julien Stainer. From wait-free to arbitrary concurrent solo executions in colorless distributed computing. Theor. Comput. Sci., 683:1-21, 2017. URL: https://doi.org/10.1016/J.TCS.2017.04.007.
  18. Maurice Herlihy and Nir Shavit. The topological structure of asynchronous computability. J. ACM, 46(6):858-923, 1999. URL: https://doi.org/10.1145/331524.331529.
  19. Annie Hui and Leila De Floriani. A two-level topological decomposition for non-manifold simplicial shapes. In Proceedings of the 2007 ACM symposium on Solid and Physical Modeling, pages 355-360, 2007. URL: https://doi.org/10.1145/1236246.1236297.
  20. Achour Mostéfaoui, Sergio Rajsbaum, and Michel Raynal. Conditions on input vectors for consensus solvability in asynchronous distributed systems. J. ACM, 50(6):922-954, 2003. URL: https://doi.org/10.1145/950620.950624.
  21. Vikram Saraph and Maurice Herlihy. The relative power of composite loop agreement tasks. In 19th International Conference on Principles of Distributed Systems, OPODIS, pages 13:1-13:16, 2015. URL: https://doi.org/10.4230/LIPICS.OPODIS.2015.13.
  22. Vikram Saraph, Maurice Herlihy, and Eli Gafni. An algorithmic approach to the asynchronous computability theorem. J. Appl. Comput. Topol., 1(3-4):451-474, 2018. URL: https://doi.org/10.1007/S41468-018-0014-4.
  23. John C. Stillwell. Classical topology and combinatorial group theory, volume 72 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1980. Google Scholar
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact