The Logical Core of Bitcoin (Part 1): Deconstructing Decentralized Transactions and Consensus from Turing Machines to Oracle Turing Machines introduction Bitcoin is not just a digital asset or payment tool, the real problem it solves is: how to achieve trust without a central arbitrator? The traditional financial system relies on central institutions such as banks and governments to ensure the legitimacy of transactions and the authority of ledgers. Bitcoin has achieved value transfer without the need for trusted third parties through blockchain technology and distributed systems. This process not only involves cryptography and game theory, but also hides a deep logical structure that can be accurately analogized to Turing machines and oracle Turing machines in computational theory. This article will reveal the two-layer structure of Bitcoin in transactions and consensus from the perspectives of formal systems and computational models: computable deterministic transactions and undecided uncertain consensus. 1、 Turing Machine: The 'computable' foundation of Bitcoin Bitcoin uses UTXO (Unspent Transaction Output) as its account model. This model is very similar to the "digital check" in reality: each transaction input must correspond to a legitimate, unspent front UTXO. To verify the validity of this transaction, the following steps need to be taken: Verify whether the digital signature matches the address; Check if the input UTXO exists and is not being used; Check if the amount is conserved (input ≥ output). All of this is done mechanically in Bitcoin nodes. This rule-based automatic operation is like formal reasoning when a Turing machine runs a program: Turing machine=a set of deterministic rules+initial input+finite control+infinite paper tape. In this sense, the transaction verification process of Bitcoin is like parallel running Turing machines, dealing with computable problems within the formal system. 2、 Oracle Turing Machine: Bitcoin's' Decisive 'Mechanism But the trading layer is only a part of Bitcoin. More importantly, the consensus layer. In a decentralized network, multiple miners may simultaneously mine blocks, forming forks. At this point, the system must make a choice: which chain is "real"? This is not a question that can be immediately answered by a deterministic algorithm. The answer depends on: Which branch will be prioritized for expansion next (i.e. continued construction by more miners); Whether the network is synchronized, propagation delay, and distribution of hash computing power. These cannot be directly known by a single node algorithm at the current moment, so Bitcoin adopts the longest chain principle as a rule: Whoever mines a longer blockchain wins This mechanism is actually doing one thing: handing over a formally undecidable question ("Which chain is the real chain?") to the computing power behavior and synchronization mechanism of the entire network to make a decision. This is just like the oracle Turing machine proposed by Turing in his doctoral thesis in 1938: In addition to the standard Turing machine, add a black box oracle that can directly make judgments on specific problems Analogously, the consensus mechanism of Bitcoin is the system's "oracle": it does not derive answers from logical deduction, but through competition, probability, and feedback mechanisms, it "selects" one from all possible states to become true history. ** 3、 The division of labor between transactions and consensus: the collaboration between Turing machines and oracles Transaction verification is the task of Turing machines: computable, logically deductive, and unambiguous; Block consensus is the task of oracle machines: requiring judgment, path selection, and dependence on network behavior; The two are fused through a block structure, where each block contains a computable set of transactions and a time node that is determined to be added to the history. Therefore, we can model the Bitcoin system as a logical architecture that operates in conjunction with the Turing machine layer and oracle layer. conclusion The Bitcoin system is neither chaotic nor mysterious. It combines the computability of formal systems with the determinacy of network behavior with a high level of abstract elegance Computable problem → Turing machine → transaction verification; Non deductive but determinable problem → oracle → consensus reached; Blockchain structure → Continuous evolution machine with dual layer combination. In the next article, we will further explore how this system evolves itself through the mechanism of "judgment confirmation expansion" during its operation, entering the deep world of what logic calls "super poor iteration" and "ordinal logic".