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 $\ell \in \{1,...,n\}$. 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.

进程匿名性已经研究了很长时间。内存匿名性是最近的。在匿名存储系统中，进程之间没有关于共享寄存器名称的先验协议。举例来说，由进程p命名为A的共享寄存器和由另一个进程q命名为B的共享寄存器可以对应于非常相同的寄存器X，而相同名称C可以对应于进程p和q的不同寄存器名称，这仍然是过程所不知道的。本文介绍完整的匿名模型，即过程和寄存器都匿名的模型。那么一个基本的问题就是“这个模型有意义吗？”，这可以翻译为“在如此薄弱的计算模型中能否解决非平凡的基本问题？”

本文肯定地回答了这个问题。更准确地说，它在这种完全匿名的模型中提出了一种无死锁的互斥算法，其中匿名寄存器是读/修改/写寄存器。该算法假设m（共享寄存器的数量）和n（进程的数量）使得m对所有整数而言都是质数$\ell \in \{\mathrm{1个}，。。。，ñ\}$。结合先前在内存匿名（但不是进程匿名）系统中互斥的结果（PODC 2019），得出这样的条件，对于完全匿名系统中这种算法的存在既有必要也有充分的条件。据我们所知，这是首次考虑完全匿名，并且在如此强大的匿名上下文中解决了非平凡的并发相关问题。