In distributed consensus research, Bitcoin is not merely a cryptographic protocol, but a super-formal system that bridges computation and philosophy.
First, the UTXO system corresponds to the deterministic Turing machine. It is a strictly consistent formal system, fully verifiable and reversible, and forms the foundation of the Bitcoin ledger.
Second, the PoW system corresponds to the non-deterministic Turing machine. The mining process is essentially an asymmetric pattern of “problem-solving vs. verification” inherent in NP problems: solving is extremely difficult, while verification is trivial. The theory of non-deterministic Turing machines abstracts this mechanism well.
What is truly unique is the time-chain system (Longest Chain Rule). It corresponds to the ordinal logic system, which follows completeness rather than consistency: it allows multiple candidate chains to coexist, and the final decision is made through the irreversibility of time. Oracle machine theory explains the choice during forks, while transfinite iteration theory ensures continuity. Together, they make Bitcoin’s time-chain a self-evolving, self-repairing order.
Thus, Bitcoin’s structure is:
The first two are consistent and reversible, while the third is inconsistent but repaired by time. Their combination makes Bitcoin a living computational entity, transcending the boundaries of traditional formal logic.
