Skip to content

P vs NP as Generator Search (Framing Note)

Status: Working Note

Scope: Careful bridge between complexity-theoretic witness search and trace-to-generator reconstruction.

Epistemic status: Formal analogy constrained to search/verification structure; not a proof claim.

Related files:

  • theory/reference/open-problems.md
  • theory/emergence/trace-to-generator.md
  • theory/core/emergence-manifesto-v1.3.md

Failure conditions:

  • Any statement implying the repository solves P vs NP.
  • Mapping complexity results directly to identity/explanation claims.

For SAT: - Instance: Boolean formula F (the trace-like constraint object). - Witness/certificate: assignment w. - Verification: check F(w)=true efficiently. - Construction/search: find such w.

If P=NP, efficient search exists whenever efficient verification exists (for NP languages).
If P≠NP, some witnesses may remain efficiently verifiable but not efficiently findable.

Why many witnesses are fine: complexity asks whether some valid witness can be found efficiently, not whether the witness is unique.

Why this differs from explanation/identity: - A satisfying assignment can verify a formula without being a unique causal history. - Engineering explanations often require runtime context, robustness, and continuity constraints beyond satisfiability.

Why this does not settle replicator/transporter debates: - Ordinary replication often executes known descriptions; it does not require universal inverse search. - Even if efficient witness search existed, that would not by itself resolve continuity-of-identity constraints in transporter scenarios.

Caution: this note does not prove or disprove P vs NP and does not reduce intelligence to that question.

Related work. The cost of generator search is formalized in Levin's universal search (1973). Practical generator recovery in constrained spaces is the working subject of program induction — Lake, Salakhutdinov & Tenenbaum (2015, Bayesian Program Learning), Ellis et al. (2021, DreamCoder) — and of open-ended symbolic regression (Schmidt & Lipson, 2009; Cranmer's PySR, 2023); Chollet (2019) frames intelligence measurement around exactly this search efficiency. The repo-internal counterpart is the inverse-reconstruction benchmark; the concept-by-concept mapping lives in the Related Work Map.