Wait-Free Solvability of Equality Negation Tasks

Authors Éric Goubault, Marijana Lazić, Jérémy Ledent, Sergio Rajsbaum

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Author Details

Éric Goubault
  • École Polytechnique, Palaiseau, France
Marijana Lazić
  • TU München, Munich, Germany
Jérémy Ledent
  • École Polytechnique, Palaiseau, France
Sergio Rajsbaum
  • Instituto de Matemáticas, UNAM, Mexico City, Mexico

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Éric Goubault, Marijana Lazić, Jérémy Ledent, and Sergio Rajsbaum. Wait-Free Solvability of Equality Negation Tasks. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We introduce a family of tasks for n processes, as a generalization of the two process equality negation task of Lo and Hadzilacos (SICOMP 2000). Each process starts the computation with a private input value taken from a finite set of possible inputs. After communicating with the other processes using immediate snapshots, the process must decide on a binary output value, 0 or 1. The specification of the task is the following: in an execution, if the set of input values is large enough, the processes should agree on the same output; if the set of inputs is small enough, the processes should disagree; and in-between these two cases, any output is allowed. Formally, this specification depends on two threshold parameters k and l, with k<l, indicating when the cardinality of the set of inputs becomes "small" or "large", respectively. We study the solvability of this task depending on those two parameters. First, we show that the task is solvable whenever k+2 <= l. For the remaining cases (l = k+1), we use various combinatorial topology techniques to obtain two impossibility results: the task is unsolvable if either k <= n/2 or n-k is odd. The remaining cases are still open.

Subject Classification

ACM Subject Classification
  • Theory of computation → Concurrency
  • Equality negation
  • distributed computability
  • combinatorial topology


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