The physical meaning of the EPR--chameleon experiment proposed in AcRe00b,AcRe01a, in which the EPR correlations are reproduced by local, independent, deterministic choices is re-examined. In addition we extend the mathematical model of AcRe00b,AcRe01a by showing that the dynamics considered there is effectively the reduced dynamics of a fully reversible evolution. We also propose a new protocol, more directly corresponding to real experiments, in which the local computers only send back to the central one the results of the evaluation of $pm1$--valued functions. The program to run the experiment is available from the WEB-page: http://volterra.mat.uniroma2.it.
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