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The Online Algorithmic Complexity Calculator




The OACC is a powerful online calculator devoted to provide estimations of algorithmic complexity (a.k.a. Kolmogorov-Chaitin complexity) (or $K$) and Algorithmic Probability for short and long strings and for 2-dimensional arrays better than any other tool, and estimations of Bennett's Logical Depth (or $LD$) for strings hitherto impossible to estimate with any other tool. These 3 measures constitute the most powerful and universal algorithmic measures of complexity. It uses a method (called $BDM$) based upon Algorithmic Probability, which is compatible with--but beyond the scope of--lossless compression algorithms that are so widely used to estimate $K$. Implementations of lossless compression are, however, entirely based upon Shannon entropy ($S$) (e.g. LZ, LZW, DEFLATE, etc) and thus cannot capture any algorithmic content beyond simple statistical patterns (repetitions).


In contrast, $BDM$ not only considers statistical regularities but is also sensitive to segments of an algorithmic nature (such as in a sequence like $12345...$), which $S$ and lossless compression algorithms would only be able to characterize as having maximum randomness and the highest degree of incompressibility. Moreover, unlike $K$ (thanks to the Invariance Theorem) both Entropy and Entropy-based compression algorithms are NOT invariant to language description and are therefore neither suitable nor robust as measures of complexity (the arguments and an example may be found here).


If you use the OACC please cite


The OACC is a project developed by the following labs:


Supported by the following institutions

Oxford University Karolinska Institute John Templeton Foundation Swedish Research Council


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