Kolmogorov Complexity Theory over the Reals
Computational Complexity
2008-03-28 v2 Symbolic Computation
Abstract
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory -- in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the BSS-machine (aka real-RAM) has been established as a major model of computation. This real realm has turned out to exhibit natural counterparts to many notions and results in classical complexity and recursion theory; although usually with considerably different proofs. The present work investigates similarities and differences between discrete and real Kolmogorov Complexity as introduced by Montana and Pardo (1998).
Keywords
Cite
@article{arxiv.0802.2027,
title = {Kolmogorov Complexity Theory over the Reals},
author = {Martin Ziegler and Wouter M. Koolen},
journal= {arXiv preprint arXiv:0802.2027},
year = {2008}
}