In theoretical computer science, there are two unavoidable cores: the Turing machine and the P vs NP problem. They not only concern the limits of algorithms, but may also touch upon the deeper laws of the physical world.

I. The Turing Machine Model

• ‍Deterministic Turing Machine (DTM): At any given step, the next operation is uniquely determined, and the computation path is single.‍
• Nondeterministic Turing Machine (NTM): At some step, the process may branch into multiple paths. As long as one of them leads to “success,” the machine accepts.
  

In theory, NTMs are more powerful than DTMs, but any NTM can be simulated by a DTM, though the cost may be exponential time.

II. P vs NP

• P problems: can be solved directly in polynomial time.
• NP problems: once a solution is given, it can be verified quickly in polynomial time.
  

The key question is: Are all “easily verifiable” problems also “easily solvable”? In other words, is P = NP? Mainstream view: P ≠ NP.

III. Two Types of Physical Manifestations of Nondeterminism

From a physical perspective, the “difficulty” of NP problems may stem from two different mechanisms:

‍Irreversible Type (process-dominated)‍

• Obtaining the solution depends on massive trial and error.
• Information is lost during the process and cannot be recovered.
• Corresponds to “dissipation” in the direction of time.
• Example: Hash collisions (Bitcoin mining).
  

Traversable Type (structure-dominated)

• The solution exists within a vast structural space.
• In theory it can be retraced, but the search is extremely inefficient.
• Corresponds to “complexity” in space.
• Example: Large number factorization (RSA encryption), Bitcoin private keys.

IV. Summary and Insights

Formally: All NTMs can be simulated by DTMs.

Physically: The hardness of NP problems may arise from time irreversibility or spatial complexity.

P vs NP is not just a mathematical puzzle—it may also reflect the connection between computation and the irreversibility of the physical world.