This cycle of papers is b%ed on the concept of generalized Boolean functions introduced by the author in the fhst article of the series. Every generalized Boolean function f : B" + B can be written in a manner similar to the canonical disjunctive form using some function defined on A x B, where A is
On generalized Boolean functions i
✍ Scribed by Nicolae Tǎndǎreanu
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 739 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper we introduce the concept of generaliz
Boolean function. Such a function has its arguments and value-s in a Boolean &&a and can be written in a manner similar to the canonical disjunctive form, but instead of the product of sim@le or complkmented variables, the product of values of certain functions is used. Every Ba~lean function is a generalized Boolea one but the converse is not true. The set of all generalized Boolean function "ge:nerated" by some fixed function is a Boolean algebra.
📜 SIMILAR VOLUMES
Suppose that G llowing corkditions: e denote &a, x) = g(b, x). (hb) b 4 G&s) = {O,l}cAcB k=2 IAl=& and F,,(g) be the set of all n variables Generalized oolean Functions e For Q oolean algebra I=m=2', we/me ~C(B)l = x3 ("; 2)(k + 2)f(m-2). k=O en nit is su#icienlly large, we have
Bent functions are the boolean functions having the maximal possible Hamming distance from the linear boolean functions. Bent functions were introduced and first studied by \(\mathrm{O}\). \(\mathrm{S}\). Rothaus in 1976 , We prove that there are exactly four symmetric bent functions on every even