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This lemma, in turn, can be used (within an induction) to prove that for every k, 0 k log N \Gamma 1, there exists an execution of 2 k+1 processes with k
 

Summary: This lemma, in turn, can be used (within an induction) to prove that for
every k, 0 ź k ź log N \Gamma 1, there exists an execution of 2 k+1 processes with k
rounds and ending with a bivalent configuration. Taking k = log N \Gamma 1 we get
the desired lower bound:
Theorem13. In the totally anonymous model, the round complexity of a pro­
tocol solving binary consensus among N processes
is\Omega (log N ).
References
1. K. Abrahamson. On achieving consensus using a shared memory. In Proceedings
of the 7th Annual ACM Symposium on Principles of Distributed Computing, pages
291--302. ACM, 1988.
2. Y. Afek, H. Attiya, D. Dolev, E. Gafni, M. Merritt, and N. Shavit. Atomic snap­
shots of shared memory. J. ACM, 40(4):873--890, Sept. 1993.
3. D. Angluin. Local and global properties in networks of processors. In Proceedings
of the 12th ACM Symposium on Theory of Computing, pages 82--93, 1980.
4. H. Attiya, M. Snir, and M. Warmuth. Computing on an anonymous ring. J. ACM,
35(4):845--876, Oct. 1988.
5. H. Brit and S. Moran. Wait­freedom vs. bounded wait­freedom in public data
structures. Universal Journal of Computer Science, pages 2--19, Jan. 1996.
6. J. E. Burns and N. A. Lynch. Bounds on shared memory for mutual exclusion.

  

Source: Attiya, Hagit - Department of Computer Science, Technion, Israel Institute of Technology

 

Collections: Computer Technologies and Information Sciences