The Complexity of Theorem-Proving Procedures

The central move

Connect efficient verification, nondeterministic computation, and polynomial reduction so one complete problem represents a whole class of apparent intractability.

Why it had to exist

Computability separated possible from impossible, but engineers also needed to distinguish feasible procedures from those whose resource growth defeats scale.

Where it leads

Computability limits → resource complexity → reductions → algorithm selection, approximation, and cryptographic assumptions.