## Abstract

Recent work established that some restricted-use objects, such as max registers, counters and atomic snapshots, admit polylogarithmic step-complexity wait-free implementations using only reads and writes: when only polynomially-many updates are allowed, reading the object (by performing a ReadMax, CounterRead or Scan operation, depending on the object's type) incurs O (log N) steps (where N is the number of processes), which was shown to be optimal. But what about the step-complexity of update operations? With these implementations, updating the object's state (by performing a WriteMax, CounterIncrement or Update operation, depending on the object's type) requires ω(log N) steps. The question that we address in this work is the following: are there read-optimal implementations of these restricted-use objects for which the asymptotic step-complexity of update operations is sub-logarithmic? We present tradeoffs between the step-complexity of read and update operations on these objects, establishing that updating a read-optimal counter or snapshot incurs ω(log N) steps. These tradeoffs hold also if compare-and-swap (CAS) operations may be used, in addition to reads and writes. We also derive a tradeoff between the step-complexities of read and update operations of M-bounded max registers: if the step-complexity of the ReadMax operation is 0(f(min(N, M))), then the step-complexity of the Write-Max operation is ω(log "Equation Presented ") . It follows from this tradeoff that the step-complexity of WriteMax in any readoptimal implementation of a max register from read, write and CAS is ω(log log/min(N, M)). On the positive side, we present a wait-free implementation of an M-bounded max register from read, write and CAS for which the step complexities of ReadMax and WriteMax operations are 0(1) and O ( log min (N, M)), respectively. Partially supported by the Israel Science Foundation (grant number 1227/10) and by the Lynne and William Frankel Center for Computing Science at Ben-Gurion University.

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 | 186-195 |

Number of pages | 10 |

ISBN (Print) | 9781450329446 |

DOIs | |

State | Published - 1 Jan 2014 |

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

### 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

- Counter
- Max register
- Restricted-use objects
- Snapshot

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications