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Turing Completeness of GNU find
The Unix command \texttt{find} is among the first commands taught to beginners, yet remains indispensable for experienced engineers. In this paper, we demonstrate that \texttt{find} possesses unexpected computational power, establishing three Turing completeness results using the GNU implementation (a standard in Linux distributions). (1) \texttt{find} + \texttt{mkdir} (a system that has only \texttt{find} and \texttt{mkdir}) is Turing complete: by encoding computational states as directory paths and using regex back-references to copy substrings, we simulate 2-tag systems. (2) GNU \texttt{find} 4.9.0+ alone is Turing complete: by reading and writing to files during traversal, we simulate a two-counter machine without \texttt{mkdir}. (3) \texttt{find} + \texttt{mkdir} without regex back-references is still Turing complete: by a trick of encoding regex patterns directly into directory names, we achieve the same power. These results place \texttt{find} among the ``surprisingly Turing-complete'' systems, highlighting the hidden complexity within seemingly simple standard utilities.
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