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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