## Abstract

A notion of a universal construction suited to distributed computing has been introduced by M. Herlihy in his celebrated paper "Wait-free synchronization" (ACM TOPLAS, 1991). A universal construction is an algorithm that can be used to wait-free implement any object defined by a sequential specification. Herlihy's paper shows that the basic system model, which supports only atomic read/write registers, has to be enriched with consensus objects to allow the design of universal constructions. The generalized notion of a k-universal construction has been recently introduced by Gafni and Guerraoui (CONCUR, 2011). A k-universal construction is an algorithm that can be used to simultaneously implement k objects (instead of just one object), with the guarantee that at least one of the k constructed objects progresses forever. While Herlihy's universal construction relies on atomic registers and consensus objects, a k-universal construction relies on atomic registers and ksimultaneous consensus objects (which have been shown to be computationally equivalent to k-set agreement objects in the read/write system model where any number of processes may crash). This paper significantly extends the universality results introduced by Herlihy and Gafni-Guerraoui. In particular, we present a k-universal construction which satisfies the following five desired properties, which are not satisfied by the previous k-universal construction: (1) among the k objects that are constructed, at least l objects (and not just one) are guaranteed to progress forever; (2) the progress condition for processes is wait-freedom, which means that each correct process executes an infinite number of operations on each object that progresses forever; (3) if one of the k constructed objects stops progressing, it stops in the same state at each process; (4) the proposed construction is contentionaware, which means that it uses only read/write registers in the absence of contention; and (5) it is indulgent with respect to the obstruction-freedom progress condition, which means that each process is able to complete any one of its pending operations on the k objects if all the other process hold still long enough. The proposed construction, which is based on new design principles, is called a (k, l)-universal construction. It uses a natural extension of k-simultaneous consensus objects, called (k, l)-simultaneous consensus objects ((k,l)-SC). Together with atomic registers, (k,l)-SC objects are shown to be necessary and sufficient for building a (k, l)-universal construction, in that sense, (k,l)-SC objects are (k,l)-universal.

Original language | English |
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Title of host publication | PODC 2014 - Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 206-208 |

Number of pages | 3 |

ISBN (Print) | 9781450329446 |

DOIs | |

State | Published - 2014 |

Externally published | Yes |

Event | 2014 ACM Symposium on Principles of Distributed Computing, PODC 2014 - Paris, France Duration: 15 Jul 2014 → 18 Jul 2014 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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### Conference

Conference | 2014 ACM Symposium on Principles of Distributed Computing, PODC 2014 |
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Country/Territory | France |

City | Paris |

Period | 15/07/14 → 18/07/14 |

## Keywords

- Asynchronous read/write system
- Crash failures
- K-set agreement
- K-simultaneous consensus
- Non-blocking
- Obstruction-freedom
- State machine replication
- Universal construction
- Wait-freedom