Numerical Evaluation of Algorithmic Complexity for Short Strings: A Glance into the Innermost Structure of Randomness
نویسندگان
چکیده
We describe a method that combines several theoretical and experimental results to numerically approximate the algorithmic (KolmogorovChaitin) complexity of all ∑ 8 n=1 2 n bit strings up to 8 bits long, and for some between 9 and 16 bits long. This is done by an exhaustive execution of all deterministic 2-symbol Turing machines with up to 4 states for which the halting times are known thanks to the Busy Beaver problem, that is 11 019 960 576 machines. An output frequency distribution is then computed, from which the algorithmic probability is calculated and the algorithmic complexity evaluated by way of the (Levin-Chaitin) coding
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عنوان ژورنال:
- Applied Mathematics and Computation
دوره 219 شماره
صفحات -
تاریخ انتشار 2012