# Weak Failures: Definitions, Algorithms and Impossibility Results

Conference paper

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## Abstract

The notion of weak failures, which should be viewed as *fractions* of traditional failures, is introduced and studied. It is known that there is no consensus algorithm using registers that can tolerate even a single crash failure. Is there a consensus algorithm using registers that can tolerate a “fraction” of a crash failure, i.e., a weak failure? It is known that there is no *k*-set consensus algorithm for \(n>k\) processes using registers that can tolerate *k* crash failures. How many weak failures can a *k*-set consensus algorithm which uses registers tolerate? Answers to these questions follow from our general possibility and impossibility results regarding the ability to tolerate weak failures.

## Keywords

Weak failures Shared memory Consensus*k*-set consensus Contention

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