Kolmogorov complexity and the Recursion Theorem
نویسندگان
چکیده
منابع مشابه
Kolmogorov Complexity and the Recursion Theorem
We introduce the concepts of complex and autocomplex sets, where a set A is complex if there is a recursive, nondecreasing and unbounded lower bound on the Kolmogorov complexity of the prefixes (of the characteristic sequence) of A, and autocomplex is defined likewise with recursive replaced by A-recursive. We observe that exactly the autocomplex sets allow to compute words of given Kolmogorov ...
متن کاملKolmogorov complexity and the second incompleteness theorem
We shall prove the second incompleteness theorem via Kolmogorov complexity.
متن کاملQuantum Kolmogorov Complexity and Information-Disturbance Theorem
In this paper, a representation of the information-disturbance theorem based on the quantum Kolmogorov complexity that was defined by P. Vitányi has been examined. In the quantum information theory, the information-disturbance relationship, which treats the trade-off relationship between information gain and its caused disturbance, is a fundamental result that is related to Heisenberg’s uncerta...
متن کاملKolmogorov Complexity and the Garden of Eden Theorem
Suppose τ is a cellular automaton over an amenable group and a finite alphabet. Celebrated Garden of Eden theorem states, that pre-injectivity of τ is equivalent to non-existence of Garden of Eden configuration. In this paper we will prove, that imposing some mild restrictions , we could add another equivalent assertion: non-existence of Garden of Eden configuration is equivalent to preservatio...
متن کاملEntropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
In classical information theory, entropy rate and algorithmic complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them a...
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: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2011-05306-7