37.5 SKADI: A 28nm Complete K-SAT Solver Featuring Dual-Path SRAM-Based Macro and Incremental Update with 100% Solvability

Zihan Wu, Xiyuan Tang, Tao Zhang, Lishan Lin, Haoyang Luo, Bocheng Xu, Zhongyi Wu, Jiahao Song, Yitao Liang, Xiaochen Bo, Yuan Wang

Abstract: Boolean satisfiability (K-SAT, K≥3) is an NP-complete problem that has applications in various fields, including electronic design automation [1], formal verification [2], and fault diagnosis [3]. The objective of the K-SAT problem is to determine whether a truth assignment exists for n Boolean variables $\mathrm{X}_{\mathrm{i}}$ to satisfy all clauses that typically are in conjunctive normal form F(x). Given its NP-complete nature, solving K-SAT problems on Von Neumann machines consumes extensive energy and time. To address this challenge, several ASIC solvers have been proposed, employing diverse methods such as continuous-time dynamics [4], Ising machines [5], and recurrent neural networks [6]. However, all prior works [4]–[8] are incomplete solvers that are only capable of resolving satisfiable (SAT) cases, without providing proof for the unsatisfiability (UNSAT) of F(x). This constraint limits their practice usage, as the satisfiability of most real-world K-SAT problems is not predetermined, requiring solvers to verify the existence of solutions for F(x). Addressing this issue necessitates a complete analysis, which encounters three key challenges: 1) Unlike incomplete solvers that solely deduce clauses from assignments, complete solvers require bidirectional deduction, i.e., solvers deduce both clauses from assignments and assignments from clauses. 2) Incomplete solvers update assignments through heuristic methods without the need to track past decisions, thereby skipping assignment management; in contrast, complete solvers rely on historical decisions to update assignments, incurring significant area costs due to storage requirements. 3) Unlike incomplete analysis that involves only 2 clause states, complete analysis requires multi-level clause states with 100% accuracy, boosting computational demand. Analog approaches to SAT solving suffer from accuracy loss, while conventional digital methods face challenges with poor area and energy efficiency.