This paper extends the concept of Karnaugh map from a logical function to a logical system, thereby allowing both the state transition graph and state transition matrix of a logical system, as well as a digital circuit, to be constructed directly. It is found that the Karnaugh map of a logical system is actually a two-dimensional state transition table or, equivalently, a table-like state transition graph and is also a grid-type state transition matrix. For constructing the state transition graph and state transition matrix of a logical system, the computational complexities of the methods based on the proposed Karnaugh map are exponentially lower than those of the existing methods. The Karnaugh maps of logical systems are then used in the analysis and design of clocked sequential circuits and in the simplification of multioutput gate circuits. Some illustrative examples and simulations are presented to demonstrate the results and their applications.

中文翻译：

---

逻辑系统的卡诺图及其在数字电路设计中的应用

本文将卡诺图的概念从逻辑函数扩展到逻辑系统，从而允许直接构造逻辑系统的状态转移图和状态转移矩阵，以及数字电路。发现逻辑系统的卡诺图实际上是一个二维状态转移表，或者等价于一个表格状的状态转移图，也是一个网格型的状态转移矩阵。为了构建逻辑系统的状态转移图和状态转移矩阵，基于所提出的卡诺图的方法的计算复杂度比现有方法呈指数级低。然后将逻辑系统的卡诺图用于时钟时序电路的分析和设计以及多输出门电路的简化。