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Theorem · computational complexity classification

FPRD-SH-T16

Policy-only local split prediction is NP-complete

Exact statement

Given an explicitly listed memoryless support policy ψ\psi and kk, deciding whether some tuple of ordinary component expressions can produce one useful canonical product state with at least kk incoming event signatures is NP-complete. Hardness holds when every letter has one support of size three.

StatusSelf-contained reduction from three-dimensional matching; exact finite reduction audit passes
External reviewNo documented external or specialist review of these FPRD results is recorded.

Context

The support graph exactly predicts worst-case local splitting, but the graph invariant need not be efficiently computable when arity and the policy are part of the input.

Hypotheses and scope

  • The support policy is represented explicitly.
  • Arity is part of the input.

Proof or evidence

Membership follows by guessing compatible signatures. For hardness, assign one fresh letter and its three-participant support to every triple in a three-dimensional matching instance; policy signatures form a clique exactly when the triples are pairwise disjoint.

NP-completeness proof →

Verification notes

All 256 subinstances of the 2-by-2-by-2 three-dimensional-matching universe preserve maximum matching size under the reduction.

Limitations

  • The hardness concerns policy-only worst-case prediction, not enumeration once a fixed canonical product is already explicit.
  • Three-dimensional matching hardness is classical; novelty is only claimed as plausible for this Boolean-product application.

Open work

Identify tractable policy classes and parameterizations for the compatibility clique number.