Bitcoin: A Total Turing Machine

Posted: 4 Nov 2018

Date Written: October 12, 2017


We demonstrate that the Bitcoin Script language allows not only for primitive recursion, but in the deployment of an Ackerman function and hence the ability to simply recurse in Bitcoin script, we show that the script system is Turing complete. From this, we introduce a new class of Turing Machine, the PTTM or probabilistic Total Turing machine and note that Bitcoin acts as a decider or Total Turing Machine which allows us to find a NIZKPoK that can act as a TM based verifier to a Non-Interactive Proof that is run on an external and non-associated TM as a proof system. Bitcoin can extend to securely offer contracts such as best fit solutions to common logistic systems and optimisation problems including the Travelling Salesman class of problems and to the optimisation of systems. This can be offered as an open or time bound contract that guarantees payment and can be solved which allowing Pseudonymity of the bidder.

Keywords: Bitcoin, Turing Complete, Decider, Script, Compiling, NIZKPoK, ZKP

Suggested Citation

Wright, Craig S, Bitcoin: A Total Turing Machine (October 12, 2017). Available at SSRN: or

Craig S Wright (Contact Author)

nChain ( email )

United Kingdom

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