Intrinsic Information Flow in Structureless NP Search

Abstract

Rather than measuring NP search in terms of Turing-machine time, we reinterpret witness recovery as an information-acquisition process: the hidden witness is the sole source of uncertainty, and identification requires sufficient reduction of this uncertainty through a rate-limited access interface in the sense of Shannon. To make this perspective explicit, we analyze an extreme regime, the \emph{psocid model}, in which the witness is accessible only via equality probes $[\pi = w^\star]$ under a uniform, structureless prior. Each probe reveals at most $O(N/2^N)$ bits of mutual information, so polynomially many probes accumulate only $o(1)$ total information. By Fano's inequality, reliable recovery requires $\Omega(N)$ bits, creating a fundamental mismatch between the information required for recovery and that obtainable through the interface. The psocid setting isolates a fully symmetric search regime in which no intermediate computation yields global eliminative leverage, thereby exposing an intrinsic informational origin of exponential search complexity.