Lower bounds for some decision problems over C

@article{Malajovich2002LowerBF,
  title={Lower bounds for some decision problems over C},
  author={Gregorio Malajovich},
  journal={Theor. Comput. Sci.},
  year={2002},
  volume={276},
  pages={425-434}
}
Lower bounds for some explicit decision problems over the complex numbers are given. The decision problems considered are certain zerodimensional subsets of N×C, and can be assimilated to a countable family of polynomials gi. More precisely, one should decide for input (i, x) if gi(x) = 0. A lower bound for deciding if a polynomial gi vanishes at some x can be derived from an uniform lower bound for the evaluation of all f ∈ (gi). That bound is obtained by means of an arithmetic invariant of… CONTINUE READING

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Combinatorial proofs for transcendency of formal power series (extended abstract)

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