Not sure what do you mean by correction algorithm? The official map itself is never corrected. Instead, the coordinates received from the GPS chipset are added by the same amount of shift (i.e. the same x'=f(x, y) and y'=g(x, y) transformation) to match the shifted map. As a result it appears no shift to the user, but the recorded track will have shifted coordinates (well, newer devices provide both coordinates before and after the addition now). The code to do the transformation is written and compiled by the government then licensed to the GPS device maker.
I am not a lawyer, but that's the common interpretation.
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