## Abstract

The power of an object type *T* can be measured as the maximum number *n* of processes that can solve consensus using only objects of *T* and registers. This number, denoted *cons*(*T*), is called the *consensus power* of *T*. This paper addresses the question of the weakest failure detector to solve consensus among a number *k* > *n* of processes that communicate using shared objects of a type *T* with consensus power *n*. In other words, we seek for a failure detector that is sufficient and necessary to “boost” the consensus power of a type *T* from *n* to *k*. It was shown in Neiger (Proceedings of the 14th annual ACM symposium on principles of distributed computing (PODC), pp. 100–109, 1995) that a certain failure detector, denoted *Ω*
_{
n
}, is sufficient to boost the power of a type *T* from *n* to *k*, and it was conjectured that *Ω*
_{
n
} was also necessary. In this paper, we prove this conjecture for *one-shot deterministic* types. We first show that, for any one-shot deterministic type *T* with *cons*(*T*) ≤ *n*, *Ω*
_{
n
} is necessary to boost the power of *T* from *n* to *n* + 1. Then we go a step further and show that *Ω*
_{
n
} is also the weakest to boost the power of (*n* + 1)-*ported* one-shot deterministic types from *n* to any *k* > *n*. Our result generalizes, in a precise sense, the result of the weakest failure detector to solve consensus in asynchronous message-passing systems (Chandra et al. in J ACM 43(4):685–722, 1996). As a corollary, we show that *Ω*
_{
t
} is the weakest failure detector to boost the *resilience* level of a distributed shared memory system, i.e., to solve consensus among *n* > *t* processes using (*t* − 1)-resilient objects of consensus power *t*.

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This paper is a revised and extended version of a paper that appeared in the Proceedings of the 17th International Symposium on Distributed Computing (DISC 2003), entitled “On failure detectors and type boosters.”

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Guerraoui, R., Kouznetsov, P. Failure detectors as type boosters.
*Distrib. Comput.* **20**, 343–358 (2008). https://doi.org/10.1007/s00446-007-0043-z

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DOI: https://doi.org/10.1007/s00446-007-0043-z

### Keywords

- Correct Process
- Reduction Algorithm
- Failure Detector
- Failure Pattern
- Shared Object