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A Rabbi Akiva Dershowitz addresses this question here. He permits it for two reasons. The first is that he says the necessity of power to maintain the writing doesn't impact the fact that it is not considered Halachic writing. He then quotes a Teshuva from Rav Asher Weiss which permits the use of a sefer with Hashem's name written on the side (such that it ...
I have consulted with R' Passow of Harvard Hillel, and he says that while there is no direct issue, there may be a problem with reading the writing, as according to Shabbat 149a, one may not read something written on a wall, nor look in a mirror on shabbat.
See the following link for a teshuvah of Bemareh Habazak vol. 5, siman 37 regarding a website operating on Shabbat: http://beta.hebrewbooks.org/pdfpager.aspx?req=43790&st=&pgnum=66 The conclusion there is that there is no problem of ma'arit ayin as it is well known that it operates automatically. The same would seem to apply to your case as well.
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