# How to simulate sequential registers from causal ones?

Background: In distributed shared memory (DSM) model, the problem of register simulations/constructions is to simulate registers with certain characteristic out of registers with weaker features. For example, we can construct the strongest multi-writer multi-reader atomic $\texttt{read/write}$ registers from the weakest single-writer multi-reader safe ones [1].

Question:

Is it possible to simulate sequential registers from causal ones in DSM model? And how to, if possible?

I guess the answer is negative. However, I have no idea how to prove/disprove it (Googling does not help on this).

[1] The Art of Multiprocessor Programming. By Maurice Herlihy and Nir Shavit (Chapter 4)

Proof: In the thesis [1], Kawash shows that causal consistency memory (with only $\texttt{read/write}$ operations) cannot solve mutual exclusion. However, Lamport's bakery algorithm (wiki), when run on sequential consistency memories, solves mutual exclusion.