25.1 A Physics-Inspired Oscillator-Based Mixed-Signal Optimization Engine for Solving 50-Variable 218-Clause 3-SAT Problems with 100% Solvability and 31.7μs Solution Time

The Boolean satisfiability (SAT) problem is a fundamental NP-complete problem, and efficiently solving it would revolutionize fields like optimization, artificial intelligence, cryptography, software, and hardware verification. Physics-inspired computers offer significant advantages, including continuous-time (CT) operation, massive parallelism, and increased energy efficiency. Solvers that map the optimization objective to a dynamical system of spins [1] have been shown to outperform classical discrete optimization solvers. Recent work maps 3-SAT to systems of coupled spins but suffers from long solution times or low solvability [2], [3], and is limited to problems with only 20 variables [3]. [4] decomposes 3-SAT problems to an all-to-all connected analog lsing machine, but the proposed iterative compute scheme results in ms-level solution times. A digital solver based on an array of processing elements (PEs) [5] has reported competitive performance, but it does not account for the substantial preprocessing time and energy required to embed the problem into the available hardware - embedding itself is a complex optimization problem. Furthermore, the system in [5] can connect only up to 32 clauses to a given variable, limiting its ability to solve real-world satisfiability problems where some spins are highly connected.