Problem 5.2: τ-Classification of Complexity

Determine if problem Π belongs to P or NP based on its η-τ signature.

function complexity_class(Π, threshold=2.0):
# Extract Coulon parameters from problem structure
η_signature = compute_η_signature(Π)
τ_level = compute_τ_level(Π)

# Critical η criterion from Coulon Theory
if max(η_signature) < threshold and τ_level ≤ 5:
    return "P"
elif any(η > threshold for η in η_signature) and τ_level ≥ 5:
    return "NP-complete"
else:
    return "NP-intermediate"