## Abstract

A notion of a universal construction suited to distributed computing has been introduced by Herlihy in his celebrated paper “Wait-free synchronization” (ACM Trans Program Lang Syst 13(1):124–149, 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 (Proceedings of 22nd international conference on concurrency theory (CONCUR’11), Springer LNCS 6901, pp 17–27, 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 k-simultaneous consensus objects (which are wait-free equivalent to k-set agreement objects in the read/write system model). 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 leastℓ 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 any of the k constructed objects stops progressing, all its copies (one at each process) stop in the same state; (4) the proposed construction is contention-aware, in the sense that it uses only read/write registers in the absence of contention; and (5) it is generous 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 processes 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, and, in that sense, (k, ℓ) -SC objects are (k, ℓ) -universal.

Original language | English |
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Pages (from-to) | 502-535 |

Number of pages | 34 |

Journal | Algorithmica |

Volume | 76 |

Issue number | 2 |

DOIs | |

State | Published - 1 Oct 2016 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2015, Springer Science+Business Media New York.

## Keywords

- Asynchronous read/write system
- Consensus
- Contention-awareness
- Crash failures
- Distributed computability
- Obstruction-freedom
- State machine replication
- Universal construction
- Wait-freedom
- k-Set agreement
- k-Simultaneous consensus