Satisfiability Modulo Theories (SMT) and SAT solvers are critical components in many formal software tools, primarily due to the fact that they are able to easily solve logical problem instances with millions of variables and clauses. This efficiency of solvers is in surprising contrast to the traditional complexity theory position that the problems that these solvers address are believed to be hard in the worst case. In an attempt to resolve this apparent discrepancy between theory and practice, theorists have proposed the study of these solvers as proof systems that would enable establishing appropriate lower and upper bounds on their complexity. For example, in recent years it has been shown that (idealized models of) SAT solvers are polynomially equivalent to the general resolution proof system for propositional logic, and SMT solvers that use the CDCL(T) architecture are polynomially equivalent to the Res*(T) proof system. In this paper, we extend this program to the MCSAT approach for SMT solving by showing that the MCSAT architecture is polynomially equivalent to the Res*(T) proof system. Thus, we establish an equivalence between CDCL(T) and MCSAT from a proof-complexity theoretic point of view. This is a first and essential step towards a richer theory that may help (parametrically) characterize the kinds of formulas for which MCSAT-based SMT solvers can perform well.

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关于MCSAT的证明复杂度

可满足性模理论 (SMT) 和 SAT 求解器是许多正式软件工具中的关键组件，主要是因为它们能够轻松解决具有数百万个变量和子句的逻辑问题实例。求解器的这种效率与传统的复杂性理论立场形成了惊人的对比，传统的复杂性理论立场认为，这些求解器解决的问题在最坏的情况下很难解决。为了解决理论与实践之间的这种明显差异，理论家们提议将这些求解器作为证明系统进行研究，从而能够为其复杂性建立适当的下限和上限。例如，近年来已经表明（理想化模型）SAT 求解器在多项式上等价于命题逻辑的一般解析证明系统，和使用 CDCL(T) 架构的 SMT 求解器在多项式上等效于 Res*(T) 证明系统。在本文中，我们通过展示 MCSAT 架构在多项式上等效于 Res*(T) 证明系统，将此程序扩展到用于 SMT 求解的 MCSAT 方法。因此，我们从证明复杂性理论的角度建立了 CDCL(T) 和 MCSAT 之间的等价关系。这是迈向更丰富理论的第一步，也是必不可少的一步，该理论可能有助于（参数化）表征基于 MCSAT 的 SMT 求解器可以很好地执行的公式种类。我们从证明复杂性理论的角度建立了 CDCL(T) 和 MCSAT 之间的等价关系。这是迈向更丰富理论的第一步，也是必不可少的一步，该理论可能有助于（参数化）表征基于 MCSAT 的 SMT 求解器可以很好地执行的公式种类。我们从证明复杂性理论的角度建立了 CDCL(T) 和 MCSAT 之间的等价关系。这是迈向更丰富理论的第一步，也是必不可少的一步，该理论可能有助于（参数化）表征基于 MCSAT 的 SMT 求解器可以很好地执行的公式种类。