Information Redistribution Under Reductions in NP Search
For theoretical computer scientists, this offers a new perspective on reductions and search algorithms, but it is purely conceptual and lacks empirical validation.
This exploratory work proposes a conceptual framework for understanding how reductions in NP search problems redistribute hidden witness information across enlarged representations, potentially improving local inferability. No concrete results or numbers are provided.
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.