Functions Definable by Arithmetic Circuits

@inproceedings{PrattHartmann2009FunctionsDB,
  title={Functions Definable by Arithmetic Circuits},
  author={Ian Pratt-Hartmann and Ivo D{\"u}ntsch},
  booktitle={CiE},
  year={2009}
}
An arithmetic circuit is a labelled, directed, acyclic graph specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. In this paper, we consider the definability of functions from tuples of sets of non-negative integers to sets of non-negative integers by means of arithmetic circuits. We prove two negative results: the first shows, roughly, that a function is not circuit-definable if it has an infinite range and sub-linear growth; the second… 
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