Nonreducible Descriptions for the Conditional Kolmogorov Complexity
نویسندگان
چکیده
منابع مشابه
Non-reducible Descriptions for Conditional Kolmogorov Complexity
Assume that a program p on input a outputs b. We are looking for a shorter program q having the same property (q(a) = b). In addition, we want q to be simple conditional to p (this means that the conditional Kolmogorov complexity K (q|p) is negligible). In the present paper, we prove that sometimes there is no such program q, even in the case when the complexity of p is much bigger than K (b|a)...
متن کاملQuantum Kolmogorov Complexity Based on Classical Descriptions
We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity coincides with the classical Kolmogorov complexity on the classical domain. Quantum Kolmogorov complexity is upper bounded and can be effectively approximated f...
متن کاملConditional Kolmogorov complexity and universal probability
The conditional in conditional Kolmogorov complexity commonly is taken to be a finite binary string. The Coding Theorem of L.A. Levin connects unconditional prefix Kolmogorov complexity with the discrete universal distribution. The least upper semicomputable code-length is up to a constant equal to the negative logarithm of the greatest lower semicomputable probability mass function. We investi...
متن کاملA CONDITIONAL KOLMOGOROV TEST by
1997 The copyright to this Article is held by the Econometric Society. It may be downloaded, printed and reproduced only for educational or research purposes, including use in course packs. No downloading or copying may be done for any commercial purpose without the explicit permission of the Econometric Society. For such commercial purposes contact the Office of the Econometric Society (contac...
متن کاملChapter 19 Kolmogorov Complexity
Kolmogorov complexity has intellectual roots in the areas of information theory, computability theory and probability theory. Despites its remarkably simple basis, it has some striking applications in Complexity Theory. The subject was developed by the Russian mathematician Andrei N. Kolmogorov (1903–1987) as an approach to the notion of random sequences and to provide an algorithmic approach t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Problems of Information Transmission
سال: 2005
ISSN: 0032-9460,1608-3253
DOI: 10.1007/s11122-005-0028-0