Universal formula estimates computational complexity using structural barriers and residual entropy, highlighting implications for cryptography and decision problems.
We present a universal formula for computational complexity based on two fundamental sources: structural barrier (γ) and residual entropy (H_res). The formula Λ_struct = n - γ_eff - H_res unifies previously disparate results including cascade inversions, bounded treewidth problems, 2-SAT, and random oracle complexity. We show that all components are computable in polynomial time from the problem description, providing a practical framework for complexity estimation. The formula explains why cryptographic constructions are hard (high γ), why random search is hard (high H_res), and why structured problems like 2-SAT are easy (both low). We verify the formula against all known complexity results and discuss implications for the P vs NP problem. Key Result: L = 2γ_eff + H_res, where complexity arises from exactly two sources: structural barrier and residual entropy.
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Aliaksei Naboko (2026) studied this question.
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