The safe-consensus task was introduced by Afek, Gafni and Lieber (DISC' 09) as a weakening of the classic consensus. When there is concurrency, the consensus output can be arbitrary, not even the input of any process. They showed that safe-consensus is equivalent to consensus, in a wait-free system. We study the solvability of consensus in three shared memory iterated models extended with the power of safe-consensus black boxes. In the first iterated model, for the $i$-th iteration, the processes write to memory, then they snapshot it and finally they invoke safe-consensus boxes. We prove that in this model, consensus cannot be implemented. In a second iterated model, processes first invoke safe-consensus, then they write to memory and finally they snapshot it. We show that this model is equivalent to the previous model and thus consensus cannot be implemented. In the last iterated model, processes write to the memory, invoke safe-consensus boxes and finally they snapshot the memory. We show that in this model, any wait-free implementation of consensus requires $\binom{n}{2}$ safe-consensus black-boxes and this bound is tight.
翻译:Afek, Gafni 和 Lieber (DISC' 09) 提出了安全协商一致的任务,作为传统共识的削弱。 当出现共通时, 协商一致产出可以是任意的, 甚至是任何进程的投入。 它们表明, 安全协商一致在无等待的系统中相当于共识。 我们研究了三个共同记忆的重复模式中的共识的可溶性, 三个共同记忆模式扩展了安全协商一致的黑盒的力量。 在第一个迭代模式中, 以美元为代谢, 程序写到记忆中, 然后他们拍下来, 最后他们引用安全协商一致的框。 我们证明, 在这种模式中, 无法执行协商一致。 在第二个迭代模式中, 程序首先引用安全协商一致, 然后将它们写到记忆中, 最后, 我们显示, 这个模式相当于前一个模式, 写到记忆中, 程序, 引用安全一致的框, 并最终勾画出记忆中。 我们在这个模式中显示, 任何不等待和紧紧紧锁的共识 需要这个协议 。