Transformations of Self-Stabilizing Algorithms
In this paper, we are interested in transformations of self-stabilizing algorithms from one model to another that preserve stabilization. We propose an easy technique for proving correctness of a natural class of transformations of self-stabilizing algorithms from any model to any other. We present a new transformation of self-stabilizing algorithms from a message passing model to a shared memory model with a finite number of registers of bounded size and processors of bounded memory and prove it correct using our technique. This transformation is not wait-free, but we prove that no such transformation can be wait-free. For our transformation, we use a new self-stabilizing token-passing algorithm for the shared memory model. This algorithm stabilizes in O(n log2 n) rounds, which improves existing algorithms.
KeywordsLocal Memory Program Counter Simulation Cycle Auxiliary Operation Output Operation
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- 1.Attiya. Efficient and robust sharing of memory in message-passing systems. In WDAG: International Workshop on Distributed Algorithms. LNCS, Springer-Verlag, 1996.Google Scholar
- 2.Attiya and Welch. Sequential consistency versus linearizability (extended abstract). In SPAA: Annual ACM Symposium on Parallel Algorithms and Architectures, 1991.Google Scholar
- 3.H. Attiya, A. Bar-Noy, and D. Dolev. Sharing memory robustly in message-passing systems. Technical Memo MIT/LCS/TM-423, Massachusetts Institute of Technology, Laboratory for Computer Science, September 1992.Google Scholar
- 4.Hagit Attiya and Jennifer Welch. Distributed Computing: Fundamentals, Simulations, and Advanced Topics. McGraw-Hill Publishing Company, May 1998. 6.Google Scholar
- 5.Amotz Bar-Noy and Danny Dolev. Shared-memory vs. message-passing in an asynchronous distributed environment. In Piotr Rudnicki, editor, Proceedings of the 8th Annual Symposium on Principles of Distributed Computing, pages 301–318, Edmonton, AB, Canada, August 1989. ACM Press.Google Scholar
- 6.E. W. Dijkstra. Self-stabilizing systems in spite of distributed control. Communications of the Association for Computing Machinery, 17(11):643–644, November 1974.Google Scholar
- 7.Dolev, Israeli, and Moran. Self-stabilization of dynamic systems assuming only read/write atomicity. DISTCOMP: Distributed Computing, 7, 1994.Google Scholar
- 9.Shlomi Dolev, Amos Israeli, and Shlomo Moran. Resource bounds for self-stabilizing message-driven protocols. SIAM Journal on Computing, 26(1):273–290, February 1997.Google Scholar
- 10.Kleoni Ioannidou. Self-Stabilizing Transformations Between Message Passing and Shared Memory Models. Master Thesis, Department of Computer Science of University of Toronto, 2001.Google Scholar
- 11.Katz and Perry. Self-stabilizing extensioins for message-passing systems. DISTCOMP: Distributed Computing, 7, 1994.Google Scholar
- 12.Lynch and Vaandrager. Forward and backward simulations for timing-based systems. In REX: Real-Time: Theory in Practice, REX Workshop, 1991.Google Scholar