Circular nonsingular threshold transformations

✍ Scribed by Takao Ueda

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 628 KB
• Volume: 105
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(92)90147-8

✦ Synopsis

Ueda, T., Circular nonsingular threshold transformations, Discrete Mathematics 105 (1992) 249-258. Circular n-dimensional Boolean transformations are those which commute with an n-cyclic permutation of variables. A minimal Boolean transformation is the one which has the minimum number of coordinates changed by it among its equivalent transformations with respect to permutations and complementations of their variables. After general results on these concepts and nonsingular threshold transformations, seven n-dimensional (and three special 6-dimensional) nonsingular threshold transformations which are circular and minimal are listed with a proof of nonsingularity.

Finally, it is proved that they are all equivalent to threshold transformations with graphs composed of 2-cycles and fixed points.