Calculating Criticalities

@article{Bundy1996CalculatingC,
  title={Calculating Criticalities},
  author={Alan Bundy and Fausto Giunchiglia and Roberto Sebastiani and Toby Walsh},
  journal={Artif. Intell.},
  year={1996},
  volume={88},
  pages={39-67}
}
The diierence between successive iterations thus decreases by at least a constant factor after the mth iteration. 36 Note that c n+1 = f(c n). We assume that c 0 < 1 since if c 0 = 1 then c n = 1 for all n. For all l and m, it is easy to see that f(0) = 0, f(1) = c 0 and f(x) is continuous in 0; 1]. In addition, f 0 (0) = f 0 (1) = 0 and f 0 (x) > 0 for all x 2 (0; 1). Let b 1 < b 1 ::: < b k be the the xed points of f in 0; 1] (i.e. f(b i) = b i). Note that b 1 = 0 so k 1. The following… CONTINUE READING
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