Global Non-Adaptive Computation and Advice Lower Bounds for SAT

This paper studies deterministic polynomial-time algorithms for SAT whose computation is completely non-adaptive. Building on earlier work showing that NP-complete problems contain globally irreducible dependencies invisible to local analysis, it formalizes non-adaptivity as fixed circuit families with no data-dependent control flow. An advice-parameterized class GNAP/a(n) is introduced to measure how much external information is required to compensate for this limitation. Using information-theoretic counting arguments and pseudorandomness assumptions, the paper proves that uniform non-adaptive algorithms cannot decide SAT unless P = NP, and that subexponential advice is insufficient. The results demonstrate that adaptivity is an essential structural resource for efficient NP-complete computation.