The abstract theory presented centers on proving computational intractability within **NP-completeness** via polynomial-time reductions between combinatorial decision problems. The core mechanism involves transforming inputs from known NP-complete problems (such as Exact Cover) to target problems (Subset Sum and Partition), thereby establishing that a solution for the latter implies an efficient algorithm for all of **P**, contradicting standard complexity assumptions ($P \neq NP$). This theoretical framework relies on strict mathematical conditions, specifically constructing element weights using exponential functions of a parameter $L$ (where sizes are powers of $L$) to enforce unique subset combinations that mirror exact cover constraints.
The abstract theory presented centers on proving computational intractability within **NP-completeness** via polynomial-time reductions between combinatorial decision problems. The core mechanism inv…