  We propose the formal study of governed blockchains that are owned and
controlled by organizations and that neither create cryptocurrencies nor
provide any incentives to solvers of cryptographic puzzles. We view such
approaches as frameworks in which system parts, such as the cryptographic
puzzle, may be instantiated with different technology. Owners of such a
blockchain procure puzzle solvers as resources they control, and use a
mathematical model to compute optimal parameters for the cryptographic puzzle
mechanism or other parts of the blockchain. We illustrate this approach with a
use case in which blockchains record hashes of financial process transactions
to increase their trustworthiness and that of their audits. For Proof of Work
as cryptographic puzzle, we develop a detailed mathematical model to derive
MINLP optimization problems for computing optimal Proof of Work configuration
parameters that trade off potentially conflicting aspects such as availability,
resiliency, security, and cost in this governed setting. We demonstrate the
utility of such a mining calculus by solving some instances of this problem.
This experimental validation is strengthened by statistical experiments that
confirm the validity of random variables used in formulating our mathematical
model. We hope that our work may facilitate the creation of domain-specific
blockchains for a wide range of applications such as trustworthy information in
Internet of Things systems and bespoke improvements of legacy financial
services.
