Zobrazeno 1 - 10
of 574
pro vyhledávání: '"68Q30"'
Autor:
Fiedler, Jacob B., Stull, D. M.
We investigate variants of Marstrand's projection theorem that hold for sets of directions and classes of sets in $\mathbb{R}^2$. We say that a set of directions $D \subseteq\mathcal{S}^1$ is $\textit{universal}$ for a class of sets if, for every set
Externí odkaz:
http://arxiv.org/abs/2411.16001
Autor:
Titov, Ivan
Solovay reducibility $\redsolovay$ was introduced by Robert M. Solovay in 1975 via translation functions on rationals. In 2022, its totalized version $\redsolovaytotal$ (i.e., Solovay reducibility via a total function on rationals) has been examined
Externí odkaz:
http://arxiv.org/abs/2410.15563
Autor:
Li, Ang
An infinite binary sequence is Bennett deep if, for any computable time bound, the difference between the time-bounded prefix-free Kolmogorov complexity and the prefix-free Kolmogorov complexity of its initial segments is eventually unbounded. It is
Externí odkaz:
http://arxiv.org/abs/2409.00631
For extending CT field-of-view to perform non-destructive testing, the Symmetric Multi-Linear trajectory Computed Tomography (SMLCT) has been developed as a successful example of non-standard CT scanning modes. However, inevitable geometric errors ca
Externí odkaz:
http://arxiv.org/abs/2408.15069
Autor:
Reimann, Jan
Publikováno v:
Structure and Randomness in Computability and Set Theory, edited by D. Cenzer, C. Porter, and J. Zapletal, pp 111-151, World Scientific, 2020
This paper surveys work on the relation between fractal dimensions and algorithmic information theory over the past thirty years. It covers the basic development of prefix-free Kolmogorov complexity from an information theoretic point of view, before
Externí odkaz:
http://arxiv.org/abs/2408.05121
Autor:
Titov, Ivan
The original notion of Solovay reducibility was introduced by Robert M. Solovay (unpublished notes) in 1975 as a measure of relative randomness. The S2a-reducibility introduced by Xizhong Zheng and Robert Rettinger (DOI:10.1007/978-3-540-27798-9_39)
Externí odkaz:
http://arxiv.org/abs/2408.04074
Autor:
Merkle, Wolfgang, Titov, Ivan
While the set of Martin-L\"of random left-c.e. reals is equal to the maximum degree of Solovay reducibility, Miyabe, Nies and Stephan(DOI:10.4115/jla.2018.10.3) have shown that the left-c.e. Schnorr random reals are not closed upwards under Solovay r
Externí odkaz:
http://arxiv.org/abs/2407.14869
Autor:
Titov, Ivan
By a celebrated result of Ku\v{c}era and Slaman (DOI:10.1137/S0097539799357441), the Martin-L\"of random left-c.e. reals form the highest left-c.e. Solovay degree. Barmpalias and Lewis-Pye (arXiv:1604.00216) strengthened this result by showing that,
Externí odkaz:
http://arxiv.org/abs/2407.14445
Autor:
Chaiken, Seth
Consider edge colorings of digraphs where edges $v_1 v_2$ and $v_2 v_3$ have different colors. This coloring induces a vertex coloring by sets of edge colors, in which edge $v_1 v_2$ in the graph implies that the set color of $v_1$ contains an elemen
Externí odkaz:
http://arxiv.org/abs/2407.06299
Autor:
Ruparel, Hemil, Mondal, Nabarun
In this paper we formally analyze the software methodology called (iterated) Test Driven Development (TDD). We formally define Specification, Software, Testing, Equivalence Partitions, Coupling, to argue about the nature of the software development i
Externí odkaz:
http://arxiv.org/abs/2407.12839