In a seminal work, Golab et al. showed that a randomized algorithm that works with atomic objects may lose some of its properties if we replace the atomic objects that it uses with linearizable objects. It was not known whether the properties that can be lost include the important property of termination (with probability 1). In this paper, we first show that, for randomized algorithms, termination can indeed be lost. Golab et al. also introduced strong linearizability, and proved that strongly linearizable objects can be used as if they were atomic objects, even for randomized algorithms: they preserve the algorithm's correctness properties, including termination. Unfortunately, there are important cases where strong linearizability is impossible to achieve. In particular, Helmi et al. MWMR registers do not have strongly linearizable implementations from SWMR registers. So we propose a new type of register linearizability, called write strong-linearizability, that is strictly stronger than linearizability but strictly weaker than strong linearizability. We prove that some randomized algorithms that fail to terminate with linearizable registers, work with write strongly-linearizable ones. In other words, there are cases where linearizability is not sufficient but write strong-linearizability is. In contrast to the impossibility result mentioned above, we prove that write strongly-linearizable MWMR registers are implementable from SWMR registers. Achieving write strong-linearizability, however, is harder than achieving just linearizability: we give a simple implementation of MWMR registers from SWMR registers and we prove that this implementation is linearizable but not write strongly-linearizable. Finally, we prove that any linearizable implementation of SWMR registers is necessarily write strongly-linearizable; this holds for shared-memory, message-passing, and hybrid systems.

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关于寄存器线性化和终止

在一项开创性的工作中，Golab等人。表明，如果我们用线性化对象替换原子对象，则适用于原子对象的随机算法可能会失去其某些属性。尚不知道可以丢失的属性是否包括终止的重要属性（概率为1）。在本文中，我们首先表明，对于随机算法，终止确实会丢失。Golab等。还引入了强大的线性化能力，并证明即使对于随机算法，也可以将强大的线性化对象当作原子对象使用：它们保留了算法的正确性，包括终止。不幸的是，在重要的情况下，无法实现强大的线性化能力。特别是，Helmi等。MWMR寄存器没有来自SWMR寄存器的强线性化实现。因此，我们提出了一种新型的寄存器线性化能力，称为写强线性化能力，它比线性化能力严格更强，但比强线性化能力完全弱。我们证明了一些不能以线性化寄存器终止的随机算法，可以与写强线性化算法一起使用。换句话说，在某些情况下线性化能力不足，但写入强线性化能力却足够。与上面提到的不可能结果相反，我们证明了可以从SWMR寄存器实现写入高度线性化的MWMR寄存器。但是，实现写强线性化要比仅实现线性化要难得多：我们从SWMR寄存器中给出了MWMR寄存器的简单实现，我们证明了该实现是线性的，但不能写强线性的。最后，我们证明SWMR寄存器的任何线性化实现都必须写强线性化。这适用于共享内存，消息传递和混合系统。