Auxiliary-unary MINKT instances -- definitions

This layer identifies the auxiliary-unary distribution's seed-level sample with the canonical MINKT instance it encodes. Keeping this map named avoids re-decoding (x, 1^t) in every average-case theorem.

def Complexity.AuxiliaryUnarySeed.minktInstance {m : ℕ} (seed : AuxiliaryUnarySeed m) : MINKT.Instance

The canonical MINKT instance sampled by an auxiliary-unary seed.

Equations

• seed.minktInstance = { output := seed.binary, time := m - seed.split }

noncomputable def Complexity.FiniteEnsemble.auxiliaryUnaryMINKTProbability {tapes : ℕ} (machine : TM tapes) (threshold : ℕ → ℕ) (m : ℕ) : ℚ

Exact probability that the positive or totalized auxiliary-unary slice is a strict MINKT yes-instance. Classical decidability is confined to this finite enumeration boundary.

Equations

• One or more equations did not get rendered due to their size.