The fixing groups for the 2-asummable Boolean functions

✍ Scribed by Takao Ueda

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 749 KB
• Volume: 20
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(77)90045-0

✦ Synopsis

The prmcipal result in thus paper ia as fc~llows. 1x1 f be a positive 2-asummahlc &;ulr~n function of n variables X,, . . ., X,. Then N ~2 {I,. . ., n] is partitioned into sets N,, _ . . Nk such that the group of permutations of N that leave j invariant IS the direct pwduct of the symmetric groups of the N,. l%e. proof is made by a strong USC c)f a charactcriration of Lasummab!! functions by Yajima and Ibaraki.

Let Q denote the set which consists of the two ,alues 0 and 1 and 0" dcncrle the cartesian n-product of Q. A Boolttan ~unctian of n variables is a functio:l defined on Q" with value in C?. The projection e, defined by e, (X) = X, and its negation Z, defined by Z, (X) = I --X, for every X = (X,, . . ., X,,) in Q" are identified with variable X, and its negation .%, respectively; X, and I?, are called literals. A torrn is a Boolean product of literals in which far each i either X, or 2, is present as a