Randomized consensus with regular registers

The well-known randomized consensus algorithm by Aspnes and Herlihy for asynchronous shared-memory systems was proved to work, even against a strong adversary, under the assumption that registers it uses are atomic registers. With registers, every read or write operation is instantaneous (and thus indivisible). As pointed out Golab et al. (2011), however, works with does not necessarily work if we replace linearizable implementations of This raises following question: still adversary its registers? We show answer affirmative, in fact, necessary. More precisely, prove only regular