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Relaxed Queues and Stacks from Read/Write Operations

Authors Armando Castañeda, Sergio Rajsbaum, Michel Raynal



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Armando Castañeda
  • Instituto de Matemáticas, UNAM, Mexico City, Mexico
Sergio Rajsbaum
  • Instituto de Matemáticas, UNAM, Mexico City, Mexico
Michel Raynal
  • Institut Universitaire de France, IRISA-Université de Rennes, France
  • Polytechnic University of Hong Kong, Hong Kong

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Armando Castañeda, Sergio Rajsbaum, and Michel Raynal. Relaxed Queues and Stacks from Read/Write Operations. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 13:1-13:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.OPODIS.2020.13

Abstract

Considering asynchronous shared memory systems in which any number of processes may crash, this work identifies and formally defines relaxations of queues and stacks that can be non-blocking or wait-free while being implemented using only read/write operations. Set-linearizability and Interval-linearizability are used to specify the relaxations formally, and precisely identify the subset of executions which preserve the original sequential behavior. The relaxations allow for an item to be returned more than once by different operations, but only in case of concurrency; we call such a property multiplicity. The stack implementation is wait-free, while the queue implementation is non-blocking. Interval-linearizability is used to describe a queue with multiplicity, with the additional relaxation that a dequeue operation can return weak-empty, which means that the queue might be empty. We present a read/write wait-free interval-linearizable algorithm of a concurrent queue. As far as we know, this work is the first that provides formalizations of the notions of multiplicity and weak-emptiness, which can be implemented on top of read/write registers only.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Computing methodologies → Distributed algorithms
  • Computing methodologies → Concurrent algorithms
  • Theory of computation → Concurrent algorithms
  • Theory of computation → Distributed algorithms
Keywords
  • Asynchrony
  • Correctness condition
  • Linearizability
  • Nonblocking
  • Process crash
  • Relaxed data type
  • Set-linearizability
  • Wait-freedom
  • Work-stealing

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