Abstract
In centralized computing we can compute a function composing a sequence of elementary functions, where the output of the i-th function in the sequence is the input to the i + 1-st function in the sequence. This computation is done without persistent registers that could store information of the outcomes of these function invocations. In distributed computing, a task is the analogue of a function. An iterated model is defined by some base set of tasks. Processes invoke a sequence of tasks from this set. Each process invokes the i + 1-st task with its output from the i-th task. Processes access the sequence of tasks, one-by-one, in the same order, and asynchronously. Any number of processes can crash. In the most basic iterated model the base tasks are read/write registers. Previous papers have studied this and other iterated models with more powerful base tasks or enriched with failure detectors, which have been useful to prove impossibility results and to design algorithms, due to the elegant recursive structure of the runs. This talk surveys results in this area, contributed mainly by Borowsky, Gafni, Herlihy, Raynal, Travers and the author.
Partially supported by PAPIIT and PAPIME UNAM projects.
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References
Afek, Y., Attiya, H., Dolev, D., Gafni, E., Merritt, M., Shavit, N.: Atomic Snapshots of Shared Memory. J. ACM 40(4), 873–890 (1993)
Attiya, H., Bar-Noy, A., Dolev, D.: Sharing Memory Robustly in Message Passing Systems. J. ACM 42(1), 124–142 (1995)
Attiya, H., Censor, K.: Tight bounds for asynchronous randomized consensus. J. ACM 55(5) (2008)
Attiya, H., Bar-Noy, A., Dolev, D., Peleg, D., Reischuk, R.: Renaming in an Asynchronous Environment. Journal of the ACM 37(3), 524–548 (1990)
Awerbuch, B.: Complexity of network synchronization. J. ACM 32, 804–823 (1985)
Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations, and Advanced Topics. Wiley, Chichester (2004)
Borowsky, E., Gafni, E.: Immediate Atomic Snapshots and Fast Renaming. In: Proc. 12th ACM Symp. on Principles of Distributed Computing (PODC 1993), pp. 41–51 (1993)
Borowsky, E., Gafni, E.: Generalized FLP Impossibility Results for t-Resilient Asynchronous Computations. In: Proc. 25th ACM STOC, pp. 91–100 (1993)
Borowsky, E., Gafni, E.: A Simple Algorithmically Reasoned Characterization of Wait-free Computations. In: Proc. 16th ACM PODC, pp. 189–198 (1997)
Borowsky, E., Gafni, E., Lynch, N., Rajsbaum, S.: The BG distributed simulation algorithm. Distributed Computing 14(3), 127–146 (2001)
Biran, O., Moran, S., Zaks, S.: A Combinatorial Characterization of the Distributed 1-solvable Tasks. J. Algorithms 11, 420–440 (1990)
Chandra, T., Toueg, S.: Unreliable Failure Detectors for Reliable Distributed Systems. J. ACM 43(2), 225–267 (1996)
Chandra, T., Hadzilacos, V., Toueg, S.: The Weakest Failure Detector for Solving Consensus. J. ACM 43(4), 685–722 (1996)
Chaudhuri, S.: More Choices Allow More Faults: Set Consensus Problems in Totally Asynchronous Systems. Information and Computation 105, 132–158 (1993)
Elrad, T., Francez, N.: Decomposition of Distributed Programs into Communication-Closed Layers. Sci. Comput. Program. 2(3), 155–173 (1982)
Chou, C.-T., Gafni, E.: Understanding and Verifying Distributed Algorithms Using Stratified Decomposition. In: PODC 1988, pp. 44–65 (1988)
Dwork, C., Lynch, N., Stockmeyer, L.: Consensus in the Presence of Partial Synchrony. J. ACM 35(2), 288–323 (1988)
Fischer, M., Lynch, N., Paterson, M.: Impossibility of Distributed Consensus with One Faulty Process. J. ACM 32(2), 374–382 (1985)
Gafni, E.: Round-by-round Fault Detectors: Unifying Synchrony and Asynchrony (Extended Abstract). In: Proc. 17th ACM Symp. on Principles of Distributed Computing (PODC), pp. 143–152 (1998)
Gafni, E.: The extended BG-simulation and the characterization of t-resiliency. In: Proc. of the 41st ACM Symp. on Theory of Computing (STOC), pp. 85–92 (2009)
Gafni E., Rajsbaum S., Loopless Programming with Tasks (Manuscript November 5, 2009) (Submitted for publication)
Gafni, E., Rajsbaum, S., Herlihy, M.: Subconsensus Tasks: Renaming is Weaker than Set Agreement. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 329–338. Springer, Heidelberg (2006)
Herlihy, M., Penso, L.D.: Tight Bounds for k-Set Agreement with Limited Scope Accuracy Failure Detectors. Distributed Computing 18(2), 157–166 (2005)
Herlihy, M.P., Rajsbaum, S., Tuttle, M.: Unifying Synchronous and Asynchronous Message-Passing Models. In: Proc. 17th ACM PODC, pp. 133–142 (1998)
Herlihy, M., Shavit, N.: The Topological Structure of Asynchronous Computability. J. ACM 46(6), 858–923 (1999)
Keidar, I., Shraer, A.: Timeliness, Failure-detectors, and Consensus Performance. In: Proc. 25th ACM PODC, pp. 169–178 (2006)
Lamport, L.: On Interprocess Communication. Distributed Computing 1(2), 77–101 (1986)
Loui, M.C., Abu-Amara, H.H.: Memory Requirements for Agreement among Unreliable Asynchronous Processes. Advances in Computing Research 4, 163–183 (1987)
Lynch, N.A.: Distributed Algorithms, 872 pages. Morgan Kaufmann, San Francisco (1997)
Moses, Y., Rajsbaum, S.: A Layered Analysis of Consensus. SICOMP 31(4), 989–1021 (2002)
Mostefaoui, A., Rajsbaum, S., Raynal, M., Travers, C.: Irreducibility and Additivity of Set Agreement-oriented Failure Detector Classes. In: Proc. PODC 2006, pp. 153–162. ACM Press, New York (2006)
Rajsbaum, S., Raynal, M., Travers, C.: Failure Detectors as Schedulers. Tech. Report # 1838, IRISA, Université de Rennes, France (2007)
Rajsbaum, S., Raynal, M., Travers, C.: The Iterated Restricted Immediate Snapshot Model. Tech. Report # 1874, IRISA, Université de Rennes, France (2007)
Rajsbaum, S., Raynal, M., Travers, C.: An impossibility about failure detectors in the iterated immediate snapshot model. Inf. Process. Lett. 108(3), 160–164 (2008)
Rajsbaum, S., Raynal, M., Travers, C.: The Iterated Restricted Immediate Snapshot Model. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 487–497. Springer, Heidelberg (2008)
Saks, M., Zaharoglou, F.: Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge. SIAM Journal on Computing 29(5), 1449–1483 (2000)
Santoro, N.: Design and Analysis of Distributed Algorithms. Wiley Interscience, Hoboken (2006)
Völzer, H.: On Conspiracies and Hyperfairness in Distributed Computing. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 33–47. Springer, Heidelberg (2005)
Yang, J., Neiger, G., Gafni, E.: Structured Derivations of Consensus Algorithms for Failure Detectors. In: Proc. 17th ACM PODC, pp. 297–308 (1998)
Zieliński, P.: Anti-Omega: the Weakest Failure Detector for Set Agreement. Tech. Rep. # 694, University of Cambridge
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Rajsbaum, S. (2010). Iterated Shared Memory Models. In: López-Ortiz, A. (eds) LATIN 2010: Theoretical Informatics. LATIN 2010. Lecture Notes in Computer Science, vol 6034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12200-2_36
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DOI: https://doi.org/10.1007/978-3-642-12200-2_36
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