Kolmogorov Complexity Theory over the Reals

M. Ziegler, W.M. Koolen, ArXiv:0802.2027 (2008).

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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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arXiv:0802.2027
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Ziegler M, Koolen WM. Kolmogorov Complexity Theory over the Reals. arXiv:08022027. Published online 2008.
Ziegler, M., & Koolen, W. M. (2008). Kolmogorov Complexity Theory over the Reals. In arXiv:0802.2027.
@article{Ziegler_Koolen_2008, title={Kolmogorov Complexity Theory over the Reals}, journal={arXiv:0802.2027}, author={Ziegler, Martin and Koolen, Wouter M.}, year={2008} }
Ziegler, Martin, and Wouter M. Koolen. “Kolmogorov Complexity Theory over the Reals.” ArXiv:0802.2027, 2008.
M. Ziegler and W. M. Koolen, “Kolmogorov Complexity Theory over the Reals,” arXiv:0802.2027. 2008.
Ziegler, Martin, and Wouter M. Koolen. “Kolmogorov Complexity Theory over the Reals.” ArXiv:0802.2027, 2008.

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