Tuomo Lempiäinen
ABSTRACT
Hella et al. (PODC 2012, Distributed Computing 2015) identified seven different message-passing models of distributed computing---one of which is the port-numbering model---and provided a complete classification of their computational power relative to each other. However, their method for simulating the ability to count incoming messages causes an additive overhead of 2Δ -- 2 communication rounds, and it was not clear if this is actually optimal. In this paper we give a positive answer, by using bisimulation as our main tool: there is a matching linear-in-Δ lower bound. This closes the final gap in our understanding of the models, with respect to the number of communication rounds. By a previously identified connection to modal logic, our result has implications to the relationship between multimodal logic and graded multimodal logic.
- R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lovász, and C. Rackoff. Random walks, universal traversal sequences, and the complexity of maze problems. In Proc. 20th Annual Symposium on Foundations of Computer Science (FOCS 1979), pages 218--223. IEEE, 1979. doi:10.1109/SFCS.1979.34. Google Scholar
Digital Library
- D. Angluin. Local and global properties in networks of processors. In Proc. 12th Annual ACM Symposium on Theory of Computing (STOC 1980), pages 82--93. ACM, 1980. doi:10.1145/800141.804655. Google ScholarDigital Library
- P. Blackburn, M. de Rijke, and Y. Venema. Modal Logic, volume 53 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge, UK, 2001. Google ScholarDigital Library
- P. Blackburn, J. van Benthem, and F. Wolter, editors. Handbook of Modal Logic, volume 3 of Studies in Logic and Practical Reasoning. Elsevier, Amsterdam, NL, 2007. Google ScholarDigital Library
- P. Boldi and S. Vigna. Computing vector functions on anonymous networks. In Proc. 4th Colloquium on Structural Information and Communication Complexity (SIROCCO 1997), pages 201--214. Carleton Scientific, 1997. Google ScholarDigital Library
- P. Boldi, S. Shammah, S. Vigna, B. Codenotti, P. Gemmell, and J. Simon. Symmetry breaking in anonymous networks: characterizations. In Proc. 4th Israel Symposium on the Theory of Computing and Systems (ISTCS 1996), pages 16--26. IEEE, 1996.Google Scholar
- J. Chalopin. Algorithmique Distribuée, Calculs Locaux et Homomorphismes de Graphes. PhD thesis, LaBRI, Université Bordeaux 1, 2006.Google Scholar
- Y. Emek and R. Wattenhofer. Stone age distributed computing. In Proc. 32nd Annual ACM Symposium on Principles of Distributed Computing (PODC 2013), pages 137--146. ACM, 2013. doi:10.1145/2484239.2484244.arXiv:1202.1186. Google ScholarDigital Library
- L. Hella, M. Järvisalo, A. Kuusisto, J. Laurinharju, T. Lempiäinen, K. Luosto, J. Suomela, and J. Virtema. Weak models of distributed computing, with connections to modal logic. Distributed Computing, 28(1):31--53, 2015. doi:10.1007/s00446-013-0202-3. arXiv:1205.2051. Google ScholarDigital Library
- M. Koucký. Universal traversal sequences with backtracking. Journal of Computer and System Sciences, 65(4):717--726, 2002. doi:10.1016/S0022-0000(02)00023-5. Google ScholarDigital Library
- A. Krebs and O. Verbitsky. Universal covers, color refinement, and two-variable counting logic: lower bounds for the depth. In Proc. 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2015), pages 689--700. IEEE, 2015. doi:10.1109/LICS.2015.69.arXiv:1407.3175. Google ScholarDigital Library
- A. Kuusisto. Modal logic and distributed message passing automata. In Proc. 22nd EACSL Annual Conference on Computer Science Logic (CSL 2013), pages 452--468. Schloss Dagstuhl--Leibniz-Zentrum für Informatik, 2013. doi:10.4230/LIPIcs.CSL.2013.452.Google Scholar
- A. Kuusisto. Infinite networks, halting and local algorithms. In Proc. 5th International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2014), pages 147--160, 2014. doi:10.4204/EPTCS.161.14.Google ScholarCross Ref
- T. Lempiäinen. A classification of weak models of distributed computing. Master's thesis, Department of Mathematics and Statistics, University of Helsinki, 2014. http://hdl.handle.net/10138/144214.Google Scholar
- T. Lempiäinen. Ability to count messages is worth Θ(Δ) rounds in distributed computing, 2015. Manuscript. arXiv:1505.02322.Google Scholar
- F. Reiter. Distributed graph automata. In Proc. 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2015), pages 192--201. IEEE, 2015. doi:10.1109/LICS.2015.27. arXiv:1404.6503. Google ScholarDigital Library
- M. Yamashita and T. Kameda. Computing on anonymous networks: part I---characterizing the solvable cases. IEEE Transactions on Parallel and Distributed Systems, 7(1):69--89, 1996. doi:10.1109/71.481599. Google ScholarDigital Library
- M. Yamashita and T. Kameda. Leader election problem on networks in which processor identity numbers are not distinct. IEEE Transactions on Parallel and Distributed Systems, 10(9):878--887, 1999. doi:10.1109/71.798313. Google ScholarDigital Library
Index Terms
- Ability to Count Messages Is Worth Θ(Δ) Rounds in Distributed Computing
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