Abstract: In order to solve a large set of logic equations fast and effectively, the principle and method of converting logic equations into integer equations are elaborated according to the characteristics of logic operations. The integer equations are simplified and the general methods of solving the integer equations are given, which are the Wu Method and the Grobner Basis. Then an elimination method based on a fast polynomial multiplication algorithm is given and developed. The method can reduce the complexity significantly. Finally, the method of solving logic equations based on integer equations is applied to fault diagnosis and an example is shown to verify the method.

Key words: logic equations, integer equations, fast polynomial multiplication, fault diagnosis

摘要： 为快速有效地求解大量逻辑方程组，根据逻辑运算的特点详细阐述了将逻辑方程转化成等效整数方程的原理和方法，并对得到的整数方程进行化简，提出了整数方程组的一般求解方法，即吴方法和Grobner基理论。接着给出并完善了一种基于快速多项式乘法的消元法，大大降低了求解的复杂度，最后将基于整数方程的逻辑方程组求解方法应用于故障诊断，并举例验证。

关键词: 逻辑方程组, 整数方程, 快速多项式乘法, 故障诊断