On Some Questions of Rationality and Decidability

@article{Sontag1975OnSQ,
  title={On Some Questions of Rationality and Decidability},
  author={Eduardo D. Sontag},
  journal={J. Comput. Syst. Sci.},
  year={1975},
  volume={11},
  pages={375-381}
}
In this note we begin by resolving (in the negative) a question posed by Paz [6, Open Problem 1, p. 65] concerning the existence of an effective procedure for determining whether a recursively specified "probabilistie input-output relation" is of finite rank. To show that such an algorithm does not exist, it is enough to prove the undecidability of the corresponding problem for "probabilistic word functions" (take an input alphabet of one letter). The undecidability of rationality for general… CONTINUE READING
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