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Distributed Computing

, Volume 14, Issue 3, pp 127–146 | Cite as

The BG distributed simulation algorithm

  • E. Borowsky
  • E. Gafni
  • N. Lynch
  • S. Rajsbaum
Original articles

Abstract.

We present a shared memory algorithm that allows a set of f+1 processes to wait-free “simulate” a larger system of n processes, that may also exhibit up to f stopping failures.

Applying this simulation algorithm to the k-set-agreement problem enables conversion of an arbitrary k-fault-tolerant{\it n}-process solution for the k-set-agreement problem into a wait-free k+1-process solution for the same problem. Since the k+1-processk-set-agreement problem has been shown to have no wait-free solution [5,18,26], this transformation implies that there is no k-fault-tolerant solution to the n-process k-set-agreement problem, for any n.

More generally, the algorithm satisfies the requirements of a fault-tolerant distributed simulation.\/ The distributed simulation implements a notion of fault-tolerant reducibility\/ between decision problems. This paper defines these notions and gives examples of their application to fundamental distributed computing problems.

The algorithm is presented and verified in terms of I/O automata. The presentation has a great deal of interesting modularity, expressed by I/O automaton composition and both forward and backward simulation relations. Composition is used to include a safe agreement\/ module as a subroutine. Forward and backward simulation relations are used to view the algorithm as implementing a multi-try snapshot\/ strategy.

The main algorithm works in snapshot shared memory systems; a simple modification of the algorithm that works in read/write shared memory systems is also presented.

Key words: Distributed computing – Fault-tolerance – Simulation – Set-agreement – Consensus 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • E. Borowsky
    • 1
  • E. Gafni
    • 2
  • N. Lynch
    • 3
  • S. Rajsbaum
    • 4
  1. 1.Computer Science Department, Boston College, Chesnut Hill, MA 02467, USA (e-mail: borowsky@bc.edu) US
  2. 2.Computer Science Department, University of California, Los Angeles, CA 90024, USA (e-mail: eli@cs.ucla.edu) US
  3. 3.Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (e-mail: lynch@theory.lcs.mit.edu) US
  4. 4.Instituto de Matemáticas, UNAM, Ciudad Universitaria, D.F. 04510, México (e-mail: rajsbaum@math.unam.mx) MX

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