DocumentCode
581551
Title
Calculus of pseudo-Boolean functions
Author
Yin, Zhao ; Daizhan, Cheng
Author_Institution
Key Lab. of Syst. & Control, AMSS, Beijing, China
fYear
2012
fDate
25-27 July 2012
Firstpage
267
Lastpage
272
Abstract
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.
Keywords
Boolean functions; calculus; integral equations; matrix algebra; tensors; MacLaurin expansion; algebraic form; calculus; indefinite integral; matrix; pseudo-Boolean function; semitensor product; Boolean functions; Calculus; Game theory; Graph theory; Linear programming; Operations research; Vectors; Pseudo-Boolean function; derivative; integral; semi-tensor product;
fLanguage
English
Publisher
ieee
Conference_Titel
Control Conference (CCC), 2012 31st Chinese
Conference_Location
Hefei
ISSN
1934-1768
Print_ISBN
978-1-4673-2581-3
Type
conf
Filename
6389939
Link To Document