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arXiv · 1712.04393

A characterization of colorless anonymous $t$-resilient task computability

Carole Delporte-Gallet·Hugues Fauconnier·Sergio Rajsbaum·Nayuta Yanagisawa
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Abstract

A task is a distributed problem for $n$ processes, in which each process starts with a private input value, communicates with other processes, and eventually decides an output value. A task is colorless if each process can adopt the input or output value of another process. Colorless tasks are well studied in the non-anonymous shared-memory model where each process has a distinct identifier that can be used to access a single-writer/multi-reader shared register. In the anonymous case, where processes have no identifiers and communicate through multi-writer/multi-reader registers, there is a recent topological characterization of the colorless tasks that are solvable when any number of asynchronous processes may crash. In this paper we study the case where at most $t$ processes may crash, where $1 \le t < n$. We prove that a colorless task is $t$-resilient solvable non-anonymously if and only if it is $t$-resilient solvable anonymously. This implies a complete characterization of colorless anonymous t-resilient asynchronous task computability.

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Carole Delporte-Gallet, Hugues Fauconnier, Sergio Rajsbaum, Nayuta Yanagisawa. 2017-12-12. A characterization of colorless anonymous $t$-resilient task computability. https://arxiv.org/abs/1712.04393

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