منابع مشابه
Algorithmic Entropy of Sets
In a previous paper a theory of program size formally identical to information theory was developed. The entropy of an individual finite object was defined to be the size in bits of the smallest program for calculating it. It was shown that this is − log2 of the probability that the object is obtained by means of a program whose successive bits are chosen by flipping an unbiased coin. Here a th...
متن کامل0 Quantum Algorithmic Entropy
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (" universal probability ") as a starting point, and define complexity (an operator) as its negative logarithm. A number of properties of Kolmogorov complexity extend naturally to the new domain. Approximately , a quantum state is simple if it is within a small distance from a low-dim...
متن کاملQuantum Algorithmic Entropy
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (“universal probability”) as a starting point, and define complexity (an operator) as its negative logarithm. A number of properties of Kolmogorov complexity extend naturally to the new domain. Approximately, a quantum state is simple if it is within a small distance from a low-dimens...
متن کاملThe Insights of Algorithmic Entropy
The algorithmic entropy of a system, the length of the shortest algorithm that specifies the system’s exact state adds some missing pieces to the entropy jigsaw. Because the approach embodies the traditional entropies as a special case, problematic issues such as the coarse graining framework of the Gibbs’ entropy manifest themselves in a different and more manageable form, appearing as the des...
متن کاملAlgorithmic Randomness of Closed Sets
We investigate notions of randomness in the space C[2N] of nonempty closed subsets of {0, 1}N. A probability measure is given and a version of the Martin-Löf test for randomness is defined. Π2 random closed sets exist but there are no random Π1 closed sets. It is shown that any random closed set is perfect, has measure 0, and has box dimension log2 4 3 . A random closed set has no n-c.e. elemen...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1976
ISSN: 0898-1221
DOI: 10.1016/0898-1221(76)90016-x