Anonymous Read/Write Memory: Leader Election and De-anonymization

Theoretical Computer Science

et al. 2020

Self Cite

A new notion of anonymity was recently introduced at PODC 2017, namely, anonymity is on the names of the registers that define the shared memory. As an example, a shared register named A by a process p and a shared register named B by another process q may correspond to the very same shared register X, while the same name C may correspond to different shared registers for p and q.Considering an asynchronous n-process anonymous shared memory system, this paper is concerned by the de-anonymization of the memory, i.e., at the end of the execution of a de-anonymization algorithm, the processes must agree on the same name for each shared register, and different shared registers must have different names.To this end, the paper first addresses leader election in an anonymous memory system. Let n be the number of processes and m the size of the anonymous memory (total number of anonymous registers). It is first shown that there is no election algorithm when the number of anonymous registers is a multiple of n. Then, assuming m = α n + β, where α is a positive integer, three election algorithms are presented, which consider the cases β = 1, β = n − 1, and β ∈ M (n), respectively, where the set M (n) characterizes the values for which mutual exclusion can be solved despite memory anonymity.Once election is solved, a general (and simple) de-anonymization algorithm is presented, which takes as a subroutine any memory anonymous leader election algorithm. Hence, any instance of this algorithm works for the values of m required by the selected underlying election algorithm. As the underlying election algorithms, the de-anonymization algorithm is symmetric in the sense that process identities can only be compared for equality and requires the participation of all the processes.

“…Leader election in read/write anonymous memory systems has been recently addressed in [10,11]. As already indicated, the present article merges and extends these two papers.…”

Section: Related Worksupporting

confidence: 67%

Leader-based de-anonymization of an anonymous read/write memory

Godard

Imbs

Theoretical Computer Science

et al. 2020

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“…Leader election on top of anonymous atomic RW registers has been addressed in [8], which describes three algorithms suited to particular cases, namely, m = α × n + 1, m = α × n + (n − 1), and m ∈ M(n) \ {1}. Differently from the general algorithm presented in this article, these three algorithms are different, each leveraging the specific value of m for which it solves the leader election problem.…”

Section: Motivation Content and Related Workmentioning

confidence: 99%

“…if (reg i .phase = committing) ∧ (phase i = electing) then % move to committing phase % (4) phase i ← committing; discarded i ← ∅ (5) else if ( |reg i .discarded | = n − 1) ∧ (reg.id ⊥) % only one winner remains; return or move to committing phase % (6) if (reg i .phase = committing) (7) then return (reg.id) (8) else REG ← ⟨⊥, ∅, committing⟩…”

Section: Presentation Of the Algorithmmentioning

confidence: 99%

From Bezout's Identity to Space-Optimal Election in Anonymous Memory Systems

Godard

Imbs

Proceedings of the 39th Symposium on Principles of Distributed Computing

et al. 2020

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An anonymous shared memory REG can be seen as an array of atomic registers such that there is no a priori agreement among the processes on the names of the registers. As an example a very same physical register can be known as REG[x] by a process p and as REG[y] (where y x) by another process q. Moreover, the register known as REG[a] by a process p and the register known as REG[b] by a process q can be the same physical register. It is assumed that each process has a unique identifier that can only be compared for equality. This article is on solving the d-election problem, in which it is required to elect at least one and at most d leaders, in such an anonymous shared memory system. We notice that the 1-election problem is the familiar leader election problem.Let n be the number of processes and m the size of the anonymous memory (number of atomic registers). The article shows that the condition gcd(m, n) ≤ d is necessary and sufficient for solving the d-election problem, where communication is through read/write or read+modify+write registers. The algorithm used to prove the sufficient condition relies on Bezout's Identity -a Diophantine equation relating numbers according to their Greatest Common Divisor. Furthermore, in the process of proving the sufficient condition, it is shown that 1-leader election can be solved using only a single read/write register (which refutes a 1989 conjecture stating that three non-anonymous registers are necessary), and that the exact d-election problem, where exactly d leaders must be elected, can be solved if and only if gcd(m, n) divides d.

“…The open problem from [22], regarding the existence of a memory-anonymous two-process starvationfree mutual exclusion algorithm is still open. Leader election on top of anonymous read/write registers de-anonymization is addressed in [9].…”

Section: Foundational Resultsmentioning

confidence: 99%

Mutual exclusion in fully anonymous shared memory systems

Information Processing Letters

Taubenfeld

2020

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Process anonymity has been studied for a long time. Memory anonymity is more recent. In an anonymous memory system, there is no a priori agreement among the processes on the names of the shared registers. As an example, a shared register named A by a process p and a shared register named B by another process q may correspond to the very same register X, while the same name C may correspond to different register names for the processes p and q, and this remains unknown to the processes. This article introduces the full anonymous model, namely a model in which both the processes and the registers are anonymous. A fundamental question is then "is this model meaningful?", which can be translated as "can non-trivial fundamental problems be solved in such a very weak computing model?"This article answers this question positively. More precisely, it presents a deadlock-free mutual exclusion algorithm in such a fully anonymous model where the anonymous registers are read/modify/write registers. This algorithm assumes that m (the number of shared registers) and n (the number of processes) are such that m is relatively prime with all the integers ℓ ∈ {1, ..., n}. Combined with a previous result (PODC 2019) on mutual exclusion in memory anonymous (but not process anonymous) systems, it follows that this condition is both necessary and sufficient for the existence of such an algorithm in fully anonymous systems. As far as we know, this is the first time full anonymity is considered, and where a non-trivial concurrency-related problem is solved in such a very strong anonymity context.