On some questions of rationality and decidability. Sontag, E. *J. Comput. System Sci.*, 11(3):375–381, 1975. abstract bibtex Some results are given in the theory of rational power series over a broad class of semirings. In particular, it is shown that for unambiguous sets the notion of rationality is independent of the semiring over which representations are defined. The undecidability of the rationality of probabilistic word functions is also established.

@ARTICLE{jcss75rat,
AUTHOR = {E.D. Sontag},
JOURNAL = {J. Comput. System Sci.},
TITLE = {On some questions of rationality and decidability},
YEAR = {1975},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {375--381},
VOLUME = {11},
KEYWORDS = {theory of computing and complexity},
PDF = {../../FTPDIR/rat-dec.pdf},
ABSTRACT = { Some results are given in the theory of rational power
series over a broad class of semirings. In particular, it is shown
that for unambiguous sets the notion of rationality is independent of
the semiring over which representations are defined. The
undecidability of the rationality of probabilistic word functions is
also established. }
}

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