Stochastic Process Turing Machines
<|reference_start|>Stochastic Process Turing Machines: Computer science theory provides many different measures of complexity of a system including Kolmogorov complexity, logical depth, computational depth, and Levin complexity. However, these measures are all defined only for deterministic Turing machines, i.e., deterministic dynamics of the underlying generative process whose output we are interested in. Therefore, by construction they cannot capture complexity of the output of stochastic processes - like those in the real world. Motivated by this observation, we combine probabilistic Turing machines with a prior over the inputs to the Turing machine to define a complete stochastic process of Turing machines. We call this a stochastic process Turing machine. Stochastic process Turing machines allow us to formalize a stochastic generalization of logical depth called stochastic depth, and also to apply stochastic thermodynamics to the analysis of Turing machines. Stochastic process Turing machines and stochastic depth allow us to study the complex, stochastic systems like the human brain, societies, and evolution all from within the framework of formal computation.<|reference_end|>
@article{wolpert2024stochastic,
    title={Stochastic Process Turing Machines},
    author={David Wolpert, Jordan Scharnhorst},
    journal={arXiv preprint arXiv:2410.07131},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.07131},
    primaryClass={cs.CC cs.FL cs.LO}
}