arXiv subjects

Jing-Yuan Wei

Publications and source records attributed to Jing-Yuan Wei.

5 recordsLinked to original sources

arXiv2026

Information Accessibility Limits in Structured NP Search

We study the problem of locating violating principal minors in matrix families lying near the boundary of P-matrices. Rather than viewing this search problem purely through computational complexity, we analyze it from an information-accessibility perspective. We show that, despite strong underlying algebraic structure, the location of a violating subset may remain difficult to infer through local queries. In the sparse-violation regime, local observations typically provide only weak eliminative power, and polynomially many queries accumulate only vanishing mutual information about the hidden witness under the induced oracle model. Using mutual information and Fano's inequality, we characterize the resulting limitation on information acquisition. The analysis highlights a conceptual distinction between structure and accessibility: a problem may possess rich underlying structure while the information required to identify a hidden witness remains weakly inferable from observable responses.

cs.IT↗

arXiv2026

Topological structure and a polynomial-time solution of linear programming over the real numbers

We present an O(mn^2) algorithm for linear programming over the real numbers with n primal and m dual variables through deciding the support set a of an optimal solution. Let z and e be two 2(n+m)-tuples with z representing the primal, dual and slack variables of linear programming, and e the all-one vector. Let Z denote the region including all (tz, t) with z meeting the zero duality gap constraint, all primal and dual constraints except for the non-negativity constraints, and without limit on the real number t. Let L be the projection of Z on the hyperplane defined by t = 0. Consider a squeeze mapping involving the two variables of each complementary pair of z. The projection of e on the image of L of the mapping lies in an (n+m-1)-sphere Q centered at e/2 of a diameter whose square equals 2(n+m). The sum of the two components of a complementary pair of z in Q equals one, and Q is the circumsphere of the hypercube where each component of its vertices takes value in {0, 1}. One vertex v* called the solution vertex is the indicator vector of a. The algorithm uses squeeze mapping to move the aforementioned projection around v* along Q so that a is identified at certain position. It consists of O(n) unidimensional squeeze mappings, each of which uses O(mn) arithmetic operations.

math.OC↗

arXiv2026

Information Redistribution Under Reductions in NP Search

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.

cs.CC↗

arXiv2026

Intrinsic Information Flow in Structureless NP Search

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 $[π= w^\star]$ 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 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.

math.OC↗

arXiv2026

Intrinsic Sequentiality in P: Causal Limits of Parallel Computation

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.

math.OC↗