Stability of Multi-Valued Continuous Consensus11Preliminary Version, Some proofs are omitted from this version.

Authors:
Lior Davidovitch;Shlomi Dolev;Sergio Rajsbaum
Affiliations:
Department of Computer Science Ben-Gurion University, Beer-Sheva, 84105, Israel;Department of Computer Science Ben-Gurion University, Beer-Sheva, 84105, Israel;Instituto de Matemáticas, UNAM Ciudad Universitaria, D.F. 04510, México
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2009

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Abstract

Multi-valued consensus functions defined from a vector of inputs (and possibly the previous output) to a single output are investigated. The consensus functions are designed to tolerate t faulty inputs. Two classes of multi-valued consensus functions are defined, the exact value and the range value, which require the output to be one of the non-faulty inputs or in the range of the non-faulty inputs, respectively. The instability of consensus functions is examined, counting the maximal number of output changes along a geodesic path of input changes, a path in which each input is changed at most once. Lower and upper bounds for the instability of multi-valued consensus functions are presented. A new technique for obtaining such lower bounds, using edgewise simplex subdivision is presented.