We consider classical representations of integers: Church's function iterators, cardinal equivalence classes of sets, ordinal equivalence classes of totally ordered sets. Since programs do not work on abstract entities and require formal representations of objects, we effectivize these abstract notions in order to allow them to be computed by programs. To any such effectivized representation is then associated a notion of Kolmogorov complexity. We prove that these Kolmogorov complexities form a strict hierarchy which coincides with that obtained by relativization to jump oracles and/or allowance of infinite computations.
Publié le : 2002-07-05
Classification:
Logic,
Computer Science,
Algorithmic Information Theory,
Kolmogorov Complexity,
Recursion Theory,
[MATH.MATH-LO]Mathematics [math]/Logic [math.LO],
[INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO],
[INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]
@article{hal-00201627,
author = {Ferbus-Zanda, Marie and Grigorieff, Serge},
title = {Church, Cardinal and Ordinal Representations of Integers and Kolmogorov complexity},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00201627}
}
Ferbus-Zanda, Marie; Grigorieff, Serge. Church, Cardinal and Ordinal Representations of Integers and Kolmogorov complexity. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00201627/