Algorithmic information theory
Algorithmic information theory
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
The discovery of algorithmic probability
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
A Theory of Program Size Formally Identical to Information Theory
Journal of the ACM (JACM)
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
AGI'12 Proceedings of the 5th international conference on Artificial General Intelligence
Hi-index | 5.23 |
Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural approach to eliminate this machine-dependence. Our method is to assign algorithmic probabilities to the different computers themselves, based on the idea that ''unnatural'' computers should be hard to emulate. Therefore, we study the Markov process of universal computers randomly emulating each other. The corresponding stationary distribution, if it existed, would give a natural and machine-independent probability measure on the computers, and also on the binary strings. Unfortunately, we show that no stationary distribution exists on the set of all computers; thus, this method cannot eliminate machine-dependence. Moreover, we show that the reason for failure has a clear and interesting physical interpretation, suggesting that every other conceivable attempt to get rid of those additive constants must fail in principle, too. However, we show that restricting to some subclass of computers might help to get rid of some amount of machine-dependence in some situations, and the resulting stationary computer and string probabilities have beautiful properties.