Kolmogorov Complexity Theory over the Reals

Martin Ziegler; Wouter M. Koolen

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arXiv · 0802.2027

Kolmogorov Complexity Theory over the Reals

Martin Ziegler·Wouter M. Koolen

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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).

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Martin Ziegler, Wouter M. Koolen. 2008-03-28. Kolmogorov Complexity Theory over the Reals. https://arxiv.org/abs/0802.2027

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