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

Lior Davidovitch | Zendy; Shlomi Dolev | Zendy; Sergio Rajsbaum | Zendy

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

Author(s) -

Lior Davidovitch,

Shlomi Dolev,

Sergio Rajsbaum

Publication year - 2009

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2009.02.015

Subject(s) - simplex , mathematical proof , mathematics , range (aeronautics) , upper and lower bounds , subdivision , path (computing) , geodesic , discrete mathematics , combinatorics , computer science , mathematical analysis , geometry , materials science , archaeology , composite material , history , programming language

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

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