Kolmogorov complexities Kmax, Kmin on computable partially ordered sets
Marie Ferbus-Zanda, Serge Grigorieff · 2008
We introduce a machine free mathematical framework to get a natural formalization of some general notions of infinite computation in the context of Kolmogorov complexity. Namely, the classes Max^{X\to D}_{PR} and Max^{X\to D}_{Rec} of functions X \to D which are pointwise maximum of partial or total computable sequences of functions where D = (D,_{ct} K^{0',D}. We characterize the orders leading to each case. We also show that K^D_{min}, K^D_{max} cannot be both much smaller than K^D at any point. These results are proved in a more general setting with two orders on D, one extending the other.