# Computer Runtimes and the Length of Proofs - With an Algorithmic Probabilistic Application to Waiting Times in Automatic Theorem Proving

@inproceedings{Zenil2012ComputerRA, title={Computer Runtimes and the Length of Proofs - With an Algorithmic Probabilistic Application to Waiting Times in Automatic Theorem Proving}, author={Hector Zenil}, booktitle={Computation, Physics and Beyond}, year={2012} }

This paper is an experimental exploration of the relationship between the runtimes of Turing machines and the length of proofs in formal axiomatic systems. We compare the number of halting Turing machines of a given size to the number of provable theorems of first-order logic of a given size, and the runtime of the longest-running Turing machine of a given size to the proof length of the most-difficult-to-prove theorem of a given size. It is suggested that theorem provers are subject to the…

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