Portfolio Synergy (+33%): When deployed alongside standard solvers in a parallel portfolio, the variance-guided approach contributed to a 33% increase in the effective solve rate for time-constrained hard instances (solving 24 instances combined vs. 18 with standard heuristics alone). EDA Application: The method provides a statistical signature for Logic Closure and Switching Activity Analysis in Electronic Design Automation (EDA), identifying stable signal configurations without exhaustive simulation. Understanding the structural properties differentiating solution spaces in NP-complete problems like 3-SAT is fundamental to computational complexity. This paper unveils a universal geometric signature inherent in 3-SAT: the set of satisfying assignments (solutions) consistently exhibits significantly lower statistical variance than the set of non-satisfying assignments (failures) under simple, deterministic mappings. Challenging initial hypotheses that suggested a need for complex number-theoretic or geometric encodings, systematic experimental ablation reveals that elementary metrics robustly capture this phenomenon. Specifically, the standard deviation of sums derived from the trivial binary mapping (True→1, False→0) – the Hamming weight variance – achieves ~94.1% accuracy in distinguishing the variance profiles of solutions versus failures Algorithm Licensing All algorithmic concepts, procedures, and deterministic constructions presented in this work are licensed under the PolyForm Noncommercial License 1.0.0. This license applies universally to any realization of the algorithm, regardless of the programming language, software environment, or hardware architecture employed.Unauthorized commercial exploitation of the algorithm or its derivatives is expressly prohibited.
Pirolo Andres Sebastian (Sun,) studied this question.