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Weak Failures: Definitions, Algorithms and Impossibility Results

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Networked Systems (NETYS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 11028))

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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.

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Author information

Authors and Affiliations

  1. The Interdisciplinary Center, P.O.Box 167, 46150, Herzliya, Israel

    Gadi Taubenfeld

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  1. Gadi Taubenfeld
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Correspondence to Gadi Taubenfeld .

Editor information

Editors and Affiliations

  1. Universität Freiburg, Freiburg, Germany

    Andreas Podelski

  2. University of Rennes 1, Rennes, France

    François Taïani

A A Formal Definition of the k-Exclusion Problem

A A Formal Definition of the k-Exclusion Problem

The k-exclusion problem, which is a natural generalization of the mutual exclusion problem is to design a protocol which guarantees that up to k processes and no more may simultaneously access identical copies of the same non-sharable resource when there are several competing processes. That is, k processes are permitted to be in their critical section simultaneously. A solution is required to withstand the slow-down or even the crash (fail by stopping) of up to \(k -1\) of processes. For \(k =1\), the 1-exclusion problem is the exactly mutual exclusion problem.

To illustrate the k-exclusion problem, consider the case of buying a ticket for a bus ride. Here a resource is a seat on the bus, and the parameter k is the number of available seats. In the k-exclusion problem, a passenger needs only to make sure that there is some free seat on the bus, but not to reserve a particular seat.

More formally, it is assumed that each process is executing a sequence of instructions in an infinite loop. The instructions are divided into four continuous sections of code: the remainder, entry, critical section and exit. The k-exclusion problem is to write the code for the entry code and the exit code in such a way that the following basic requirements are satisfied.

  • k-exclusion: No more than k processes are at their critical section at the same time.

  • k-deadlock-freedom: If strictly fewer than k processes fail (are delayed forever) then if a process is trying to enter its critical section, then some process, not necessarily the same one, eventually enters its critical section.

The k-deadlock-freedom requirement may still allow “starvation” of individual processes. It is possible to consider stronger progress requirements which do not allow starvation.

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Taubenfeld, G. (2019). Weak Failures: Definitions, Algorithms and Impossibility Results. In: Podelski, A., Taïani, F. (eds) Networked Systems. NETYS 2018. Lecture Notes in Computer Science(), vol 11028. Springer, Cham. https://doi.org/10.1007/978-3-030-05529-5_4

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  • DOI: https://doi.org/10.1007/978-3-030-05529-5_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05528-8

  • Online ISBN: 978-3-030-05529-5

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