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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)

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Answer my own question: The answer is (probably; please let me know if I am wrong) negative: it is impossible to simulate sequential registers from causal registers.

Note: the following proof is indirect. And I am still interested in a direct proof.

Theorem: It is impossible to simulate sequential registers from causal registers.

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.


[1] Limitations and Capabilities of Weak Memory Consistency Systems by Jalal Y. Kawash, PhD Thesis, 2000.

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