## Abstract

The notion of an anonymous shared memory, introduced by Taubenfeld in PODC 2017, considers that processes use different names for the same memory location. As an example, a location name A used by a process p and a location name B A used by another process q can correspond to the very same memory location X, and similarly for the names B used by p and A used by q which may (or may not) correspond to the same memory location Y X. In this context, the PODC paper presented a 2-process symmetric deadlock-free mutual exclusion (mutex) algorithm and a necessary condition on the size m of the anonymous memory for the existence of such an n-process algorithm. This condition states that m must be belongs to M(n) {1} where M(n)= {m: : (1) The present paper presents two optimal deadlock-free symmetric mutual exclusion algorithms for n-process systems where communication is through m registers. The first algorithm, which considers anonymous read/write registers, works for any m which is n and belongs to the set M(n). It follows that this condition on m is both necessary and sufficient for symmetric deadlock-free mutual exclusion in this anonymity context, and this algorithm is optimal with respect to m The second algorithm, which considers anonymous read/modify/write atomic registers, works for any m M(n), which is shown to be necessary and sufficient for anonymous read/modify/write registers. It follows that, when m > 1, m M(n) is a tight characterization of the size of the anonymous shared memory needed to solve deadlock-free mutex, be the registers read/write or read/modify/write.

Original language | English |
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Title of host publication | PODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 157-166 |

Number of pages | 10 |

ISBN (Electronic) | 9781450362177 |

DOIs | |

State | Published - 16 Jul 2019 |

Externally published | Yes |

Event | 38th ACM Symposium on Principles of Distributed Computing, PODC 2019 - Toronto, Canada Duration: 29 Jul 2019 → 2 Aug 2019 |

### Publication series

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

Conference | 38th ACM Symposium on Principles of Distributed Computing, PODC 2019 |
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Country/Territory | Canada |

City | Toronto |

Period | 29/07/19 → 2/08/19 |

### Bibliographical note

Publisher Copyright:© 2019 ACM.

## Keywords

- Anonymous shared memory
- Asynchronous system
- Atomic register
- Computability
- Deadlock-freedom
- Mutual exclusion
- Read-modify-write register
- Read-write register