计算机工程与应用
計算機工程與應用
계산궤공정여응용
COMPUTER ENGINEERING AND APPLICATIONS
2015年
4期
71-75
,共5页
逻辑方程组%整数方程%快速多项式乘法%故障诊断
邏輯方程組%整數方程%快速多項式乘法%故障診斷
라집방정조%정수방정%쾌속다항식승법%고장진단
logic equations%integer equations%fast polynomial multiplication%fault diagnosis
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。
為快速有效地求解大量邏輯方程組，根據邏輯運算的特點詳細闡述瞭將邏輯方程轉化成等效整數方程的原理和方法，併對得到的整數方程進行化簡，提齣瞭整數方程組的一般求解方法，即吳方法和Grobner基理論。接著給齣併完善瞭一種基于快速多項式乘法的消元法，大大降低瞭求解的複雜度，最後將基于整數方程的邏輯方程組求解方法應用于故障診斷，併舉例驗證。
위쾌속유효지구해대량라집방정조，근거라집운산적특점상세천술료장라집방정전화성등효정수방정적원리화방법，병대득도적정수방정진행화간，제출료정수방정조적일반구해방법，즉오방법화Grobner기이론。접착급출병완선료일충기우쾌속다항식승법적소원법，대대강저료구해적복잡도，최후장기우정수방정적라집방정조구해방법응용우고장진단，병거례험증。
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.
