The K-Degrees, Low for K Degrees, and Weakly Low for K Sets
نویسنده
چکیده
We call A weakly low for K if there is a c such that KA(σ) ≥ K(σ)−c for infinitely many σ; in other words, there are infinitely many strings that A does not help compress. We prove that A is weakly low for K iff Chaitin’s Ω is A-random. This has consequences in the K-degrees and the low for K (i.e., low for random) degrees. Furthermore, we prove that the initial segment prefix-free complexity of 2-random reals is infinitely often maximal. This had previously been proved for plain Kolmogorov complexity.
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عنوان ژورنال:
- Notre Dame Journal of Formal Logic
دوره 50 شماره
صفحات -
تاریخ انتشار 2009