Stability of Multi-Valued Continuous Consensus

Lior Davidovitch, Shlomi Dolev, Sergio Rajsbaum

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)23-38
Number of pages16
JournalElectronic Notes in Theoretical Computer Science
Issue numberC
StatePublished - 24 Mar 2009


  • Fault-tolerance
  • boolean functions
  • consensus
  • sensors
  • stability

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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