Model abstraction for finite state automata is helpful for decreasing computational complexity and improving comprehensibility for the verification and control synthesis of discrete-event systems (DES). Supremal quasi-congruence equivalence is an effective method for reducing the state space of DES and its effective algorithms based on graph theory have been developed. In this paper, a new method is proposed to convert the supremal quasi-congruence computation into a binary linear programming problem which can be solved by many powerful integer linear programming and satisfiability (SAT) solvers. Partitioning states to cosets is considered as allocating states to an unknown number of cosets and the requirement of finding the coarsest quasi-congruence is equivalent to using the least number of cosets. The novelty of this paper is to solve the optimal partitioning problem as an optimal state-to-coset allocation problem. The task of finding the coarsest quasi-congruence is equivalent to the objective of finding the least number of cosets. Then the problem can be solved by optimization methods, which are respectively implemented by mixed integer linear programming (MILP) in MATLAB and binary linear programming (BLP) in CPLEX. To reduce the computation time, the translation process is first optimized by introducing fewer decision variables and simplifying constraints in the programming problem. Second, the translation process formulates a few techniques of converting logic constraints on finite automata into binary linear constraints. These techniques will be helpful for other researchers exploiting integer linear programming and SAT solvers for solving partitioning or grouping problems. Third, the computational efficiency and correctness of the proposed method are verified by two different solvers. The proposed model abstraction approach is applied to simplify the large-scale supervisor model of a manufacturing system with five automated guided vehicles. The proposed method is not only a new solution for the coarsest quasi-congruence computation, but also provides us a more intuitive understanding of the quasi-congruence relation in the supervisory control theory. A future research direction is to apply more computationally efficient solvers to compute the optimal state-to-coset allocation problem.

有限状态自动机的模型抽象有助于降低计算复杂性并提高离散事件系统（DES）验证和控制综合的可理解性。至高拟同余等价是一种减少DES状态空间的有效方法，其基于图论的有效算法已经被开发出来。本文提出了一种新方法，将至上拟同余计算转换为二元线性规划问题，该问题可以通过许多强大的整数线性规划和可满足性（SAT）求解器来解决。将状态划分为陪集被认为是将状态分配给未知数量的陪集，并且找到最粗拟同余的要求相当于使用最少数量的陪集。本文的新颖之处在于将最优划分问题作为最优状态到陪集分配问题来解决。找到最粗糙的拟同余的任务相当于找到最少数量的陪集的目标。然后可以通过优化方法来求解问题，分别通过MATLAB中的混合整数线性规划（MILP）和CPLEX中的二进制线性规划（BLP）来实现。为了减少计算时间，首先通过引入更少的决策变量并简化编程问题中的约束来优化翻译过程。其次，转换过程制定了一些将有限自动机上的逻辑约束转换为二进制线性约束的技术。这些技术将有助于其他研究人员利用整数线性规划和 SAT 求解器来解决分区或分组问题。第三，通过两种不同的求解器验证了该方法的计算效率和正确性。所提出的模型抽象方法用于简化具有五辆自动导引车的制造系统的大规模监控模型。该方法不仅为最粗糙的拟同余计算提供了一种新的解决方案，而且使我们对监督控制理论中的拟同余关系有了更直观的理解。未来的研究方向是应用计算效率更高的求解器来计算最优状态到陪集分配问题。