Paper Info
Title
Directed Projection Graph Of N-Dimensional Hypercube And Subhypercube Decomposition Of Balanced Linearly Separable Boolean Functions
Abstract
A directed projection graph of the n-dimensional hypercube on the two-dimensional plane is successfully created. Any n-variable Boolean function can be easily transformed to an induced subgraph of the projection. Therefore, the discussions on n-variable Boolean functions only need to focus on a two-dimensional planar graph. Some mathematical theories on the projection graph and the induced subgraph are established, and some properties and characteristics of a balanced linearly separable Boolean function (BLSBF) are uncovered. In particular, the sub-hypercube decompositions of BLSBF is easily represented on the projection, and meanwhile, the enumeration scheme for counting the number of n-variable BLSBFs is developed by using equivalence classification and conformal transformation. With the aid of the directed projection grap constructed in this paper, one can further study many difficult problems in some fields such as Boolean functions and artificial neural networks.
Year
DOI
Venue
2021
10.1142/S0218127421501388
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Hypercube, complexity, directed projection graph, linearly separable Boolean function (LSBF), balanced LSBF (BLSBF), hyperstar, induced subgraph, subhypercube decomposition
Journal
31
Issue
ISSN
Citations 
09
0218-1274
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Wei Jin18325.25
Fang-yue Chen28018.67
Qinbin He301.01