Boolean satisfiability (SAT) is widely used as a solver engine in electronic design automation (EDA). Typically, SAT is used to determine whether one or more groups of variables can be combined to form a true formula. All solutions SAT (AllSAT) is a variant of the SAT problem. In the fields of formal verification and pattern generation, AllSAT is particularly useful because it efficiently enumerates all possible solutions. In this paper, a semi-tensor product (STP) based AllSAT solver is proposed. The solver can solve instances described in both the conjunctive normal form (CNF) and circuit form. The implementation of our method differs from incremental enumeration because we do not add blocking conditions for existing solutions, but rather compute the matrices to obtain all the solutions in one pass. Additionally, the logical matrices support a variety of logic operations. Results from experiments with MCNC benchmarks using CNF-based and circuit-based forms show that our method can accelerate CPU time by 8.1x (238x maximum) and 19.9x (72x maximum), respectively.

布尔可满足性 (SAT) 广泛用作电子设计自动化 (EDA) 中的求解器引擎。通常，SAT 用于确定是否可以将一组或多组变量组合起来形成真正的公式。所有解决方案 SAT (AllSAT) 是 SAT 问题的变体。在形式验证和模式生成领域，AllSAT 特别有用，因为它有效地枚举了所有可能的解决方案。本文提出了一种基于半张量积（STP）的AllSAT求解器。该求解器可以求解以合取范式 (CNF) 和电路形式描述的实例。我们的方法的实现与增量枚举不同，因为我们没有为现有解决方案添加阻塞条件，而是计算矩阵以一次性获得所有解决方案。此外，逻辑矩阵支持多种逻辑运算。使用基于 CNF 和基于电路的形式进行 MCNC 基准测试的实验结果表明，我们的方法可以将 CPU 时间分别加速 8.1 倍（最大值 238 倍）和 19.9 倍（最大值 72 倍）。