The Solvability of Consensus in Iterated Models Extended with Safe-Consensus

Abstract The safe-consensus task was introduced by Afek, Gafni and Lieber (DISC’ 09) as a weakening of the classic consensus. When there is concurrency, consensus output can be arbitrary, not even input any process. They showed that equivalent to consensus, in wait-free system. We study solvability three shared memory iterated models extended with power black boxes. In first model, for i -th iteration, processes write memory, then they snapshot it finally invoke prove this cannot implemented. second safe-consensus, it. show model previous thus last boxes memory. implementation requires $$\Omega (n^{2})$$ Ω ( n 2 ) black-boxes bound tight.