Jing-Yuan Wei

Jing-Yuan Wei

Using reductions from structured P-matrix violation search to classical NP-complete formulations such as 3-SAT and Subset Sum, we examine the relationship between representational expansion, auxiliary variables, local inferability, and information accessibility. Rather than viewing reductions purely as computational transformations, we interpret them as mechanisms that redistribute hidden witness information across enlarged representations. From this perspective, reductions, gadgets, and auxiliary structures may expose globally encoded witness information to local propagation and inference, while search algorithms act as decoding procedures attempting to recover the original hidden witness. The resulting observations suggest that representational expansion may improve local inferability by introducing auxiliary variables and consistency structures, while preserving the need to recover the underlying witness information. This work is exploratory in nature and proposes a conceptual framework for understanding how reductions reshape information accessibility in NP search.

Jing-Yuan Wei

We study the problem of locating violating principal minors in structured matrix families that lie near the boundary of P-matrices and admit sparse violations under perturbation. Viewing violation search as an information acquisition problem, we show that, despite strong underlying structure, the location of a violation is globally encoded and not accessible through local queries. This leads to an information-theoretic bottleneck: each query reveals only vanishing information about the violating subset, so that polynomially many queries accumulate insufficient information to identify it. Using mutual information and Fano's inequality, we show that any algorithm restricted to polynomially many queries cannot recover the violating subset with constant success probability. Our analysis highlights a fundamental distinction between structure and accessibility: even highly structured problems can be computationally intractable when the information required to locate a solution is not accessible through the available queries.

Jing-Yuan Wei

We reinterpret NP witness discovery through an information-theoretic lens. Rather than measuring search solely by Turing-machine time, we treat recovery as an information-acquisition process: the hidden witness is the sole source of uncertainty, and identification requires reducing 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 $[π= w^\star]$ 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 $Ω(N)$ bits, creating a fundamental mismatch between required and obtainable information. The psocid setting thus isolates a fully symmetric search regime in which no intermediate computation yields global eliminative leverage, thereby exposing an informational origin of exponential search complexity.

Jing-Yuan Wei

We study a polynomial-time decision problem in which each input encodes a depth-$N$ causal execution in which a single non-duplicable token must traverse an ordered sequence of steps, revealing at most $O(1)$ bits of routing information at each step. The uncertainty in the problem lies in identifying the delivery path through the relay network rather than in the final accept/reject outcome, which is defined solely by completion of the prescribed execution. A deterministic Turing machine executes the process in $Θ(N)$ time. Using information-theoretic tools - specifically cut-set bounds for relay channels and Fano's inequality - we prove that any execution respecting the causal constraints requires $Ω(N)$ units of causal time, thereby ruling out asymptotic parallel speedup. We further show that no classical $\mathbf{NC}$ circuit family can implement the process when circuit depth is interpreted as realizable parallel time. This identifies a class of polynomial-time problems with intrinsic causal structure and highlights a gap between logical parallelism and causal executability.