Calculus of Pseudo-Boolean Functions

摘要：

The purpose of this paper is to propose a framework for the calculus of pseudo-Boolean function (PBF). Using semitensor product (STP) of matrices, this paper generalizes the calculus of Boolean functions (BF) to PBF. First, the derivative of PBF is defined. Using the algebraic form of PBFs, the formula for the derivative of a PBF is obtained. Then, the integral of a PBF is also defined as the inverse of the derivative. By generalizing the MacLaurin expansion of BF to PBF, a necessary and sufficient condition for the existence of the indefinite integral of a PBF is proved.

关键词： Pseudo-Boolean function derivative integral semi-tensor product

作者: ZHAO Yin CHENG Daizhan

作者单位: Key Lab. of Systems and Control, AMSS, Chinese Academy of Sciences, Beijing 100190

会议类型: 国际会议

会议名称: The 31st Chinese Control Conference(第三十一届中国控制会议)

会议地点: 合肥

会议语种:英文

页码: 267-272

在线出版日期: 2012-07-01（万方平台首次上网日期，不代表论文的发表时间）