Intrinsic Information Flow in Structureless NP Search

TL;DR

This paper reinterprets NP search complexity as an information acquisition problem, revealing an intrinsic informational barrier that explains exponential search difficulty in a structureless witness recovery model.

Contribution

It introduces the psocid model to analyze the informational limits of witness recovery, highlighting a fundamental mismatch between information needed and accessible.

Findings

Probes reveal only negligible information per attempt.

Reliable recovery requires linear amount of information, which is unattainable in the model.

Exposes an intrinsic informational barrier to polynomial-time 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.